The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A175492 Numbers m >= 3 such that binomial(m,3) + 1 is a square. 1
 7, 10, 24, 26, 65, 13777 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Related sequences: Numbers m such that binomial(m,2) is a square: A055997; Numbers m such that binomial(m,2) + 1 is a square: A006451 + 1; Numbers m such that binomial(m,2) - 1 is a square: A072221 + 1; Numbers m >= 3 such that binomial(m,3) is a square: {3, 4, 50} (Proved by A. J. Meyl in 1878); Numbers m >= 4 such that binomial(m,4) + 1 is a square: {6, 7, 45, 55, ...}; Numbers m >= 7 such that binomial(m,7) + 1 is a square: {8, 10, 21, 143, ...}. No additional terms up to 10 million. - Harvey P. Dale, Apr 04 2017 No additional terms up to 10 billion. - Jon E. Schoenfield, Mar 18 2022 No additional terms up to 1 trillion. The sequence is finite by Siegel's theorem on integral points. - David Radcliffe, Jan 01 2024 LINKS Table of n, a(n) for n=1..6. Wikipedia, Tetrahedral number MATHEMATICA lst = {}; k = 3; While[k < 10^6, If[ IntegerQ@ Sqrt[ Binomial[k, 3] + 1], AppendTo[lst, k]]; k++ ]; lst (* Robert G. Wilson v, Jun 11 2010 *) Select[Range[3, 14000], IntegerQ[Sqrt[Binomial[#, 3]+1]]&] (* Harvey P. Dale, Apr 04 2017 *) PROG (PARI) isok(m) = (m>=3) && issquare(binomial(m, 3)+1); \\ Michel Marcus, Mar 15 2022 (Python) from sympy import binomial from sympy.ntheory.primetest import is_square for m in range(3, 10**6): if is_square(binomial(m, 3)+1): print(m) # Mohammed Yaseen, Mar 18 2022 CROSSREFS Cf. A006451, A007318, A055997, A072221. Cf. A216268 (values of binomial(m, 3)) and A216269 (square roots of binomial(m, 3) + 1). Sequence in context: A183330 A196316 A134329 * A241052 A280173 A229310 Adjacent sequences: A175489 A175490 A175491 * A175493 A175494 A175495 KEYWORD nonn,more,fini AUTHOR Ctibor O. Zizka, May 29 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 01:42 EDT 2024. Contains 372807 sequences. (Running on oeis4.)