# 14 Oct 2015 He came across a page of formulas that Ramanujan wrote a year after he first pointed out the special qualities of the number 1729 to Hardy. By

What Ono and Trebat-Leder had discovered, in other words, was that the Hardy-Ramanujan number, 1729 was known to Ramanujan as a solution to equation 6 above, expressible as the expansion of powers of ξ, given by the coefficients α, β, γ for n = 0, namely α₀ = 9, β₀ = −12, γ₀ = −10.

No, Hardy! The number 1728 is one less than the Hardy-Ramanujan number 1729 (taxicab number) Note that the values of n s (spectral index) 0.965, of the average of the Omega mesons Regge slope 0.987428571 and of the dilaton 0.989117352243, are also connected to the following two Rogers-Ramanujan … 1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation: Ramanujan is said to have made this observation to Hardy who happened to be visiting him while he was recovering in a sanatorium in England, in the year 1918; on entering Ramanujan’s room, Hardy apparently said (perhaps just to start a conversation), “I came in a taxi whose number was 1729. It is given by The number derives its name from the following story G. H. Hardy told about Ramanujan. "Once, in the taxi from London, Hardy noticed its number, 1729. The number 1729 is known as the Hardy–Ramanujan number after a famous visit by Hardy to see Ramanujan at a hospital. In Hardy's words: I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." The Hardy-Ramanujan number stems from an anecdote wherein the British mathematician GH Hardy had gone to meet S Ramanujan in hospital. Hardy said that he came in a taxi having the number '1729', What Ono and Trebat-Leder had discovered, in other words, was that the Hardy-Ramanujan number, 1729 was known to Ramanujan as a solution to equation 6 above, expressible as the expansion of powers of ξ, given by the coefficients α, β, γ for n = 0, namely α₀ = 9, β₀ = −12, γ₀ = −10.

## Ramanujan Numbers - posted in C and C++: Hi, I have a programming assignment to display all the Ramanujan numbers less than N in a table output. A Ramanujan number is a number which is expressible as the sum of two cubes in two different ways.Input - input from keyboard, a positive integer N ( less than or equal to 1,000,000)output - output to the screen a table of Ramanujan numbers less than

This number, or rather the beauty of the number, was expounded by Srinivasa Ramanujan Iyengar, considered by  25 Aug 2007 Hi ram.patil,. A Hardy-Ramanujan number is a number which can be expressed as the sum of two positive cubes in exactly two different ways.

### What Ono and Trebat-Leder had discovered, in other words, was that the Hardy-Ramanujan number, 1729 was known to Ramanujan as a solution to equation 6 above, expressible as the expansion of powers of ξ, given by the coefficients α, β, γ for n = 0, namely α₀ = 9, β₀ = −12, γ₀ = −10. 1729 = 13 + 123 = 93 + 103. — Orpita Majumdar, via e-mail The two different ways 1729 is expressible as the sum of two cubes are 1³ + 12³ and 9³ + 10³. The number has since become known as the Hardy-Ramanujan number, the second so-called “ taxicab number ”, defined as 1729.this number is really mysterious..it follows so many properties..Hardy and Ramanujan together found so many interesting facts about this number 2015-11-03 2019-12-23 Abstract. In his famous letters of 16 January 1913 and 29 February 1913 to G. H. Hardy, Ramanujan [23, pp. xxiii-xxx, 349–353] made several assertions about prime numbers, including formulas for π(x), the number of prime numbers less than or equal to x.Some of those formulas were analyzed by Hardy , [5, pp. 234–238] in 1937.

Hint: A Hardy Ramanujan number is a popular number which can be expressed as a sum of two cubes in two ways. So, we can test each number based on this  22 Dec 2020 Number 1729 is called the Hardy-Ramanujan number — the smallest number can be expressed as the sum of two different cubes in two  1729 is the smallest Hardy– Ramanujan Number. There are an infinitely many such numbers, such as … 4104 = 2 3 + 16 3 and 4104 = 9 3  16 Oct 2015 Because of this incident, 1729 is now known as the Ramanujan-Hardy number. To date, only six taxi-cab numbers have been discovered that  27 Apr 2016 Story of Srinivasa Ramanujan, from his early self-study of math to the with Littlewood—and was being pulled in the direction of number theory  Below is the even better java code for printing N ramanujan numbers as it has even less time complexity.

I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen.

1729 is the natural number following 1728 and preceding 1730.
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### 1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the

30 apr. 2014 — Detta är (som alla mattenördar där ute redan vet) ett magiskt nummer som går under en särskild beteckning: the Hardy-Ramanujan number. Euler, Gauss, Ramanujan, and TuringNewton videos from Brady's Objectivity channelMillennium Nursery Rhymes and Numbers - with Alan Stewart. In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on  9 okt. 2017 — Vichitra Games presents a new and unique puzzle 'Mystery Numbers'. Inspired by legendary mathematician Ramanujan. Ramanujan created a  1) Peter Olofsson.