A216268
Tetrahedral numbers of the form k^2 - 1.
Original entry on oeis.org
0, 35, 120, 2024, 2600, 43680, 435730689800
Offset: 1
Cf.
A003556 (both square and tetrahedral).
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select(t -> issqr(t+1), [seq(i*(i+1)*(i+2)/6, i=0..10^6)]); # Robert Israel, Jan 02 2024
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t = {}; Do[tet = n (n + 1) (n + 2)/6; If[IntegerQ[Sqrt[tet + 1]], AppendTo[t, tet]], {n, 0, 100000}]; t (* T. D. Noe, Mar 18 2013 *)
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A000292(n) = n*(n+1)*(n+2)\6;
for(n=0,10^9, t=A000292(n); if (issquare(t+1), print1(t,", ") ) );
/* Joerg Arndt, Mar 16 2013 */
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import math
for i in range(1<<33):
t = i*(i+1)*(i+2)//6 + 1
sr = math.isqrt(t)
if sr*sr == t:
print (t-1, sep=' ')
A175492
Numbers m >= 3 such that binomial(m,3) + 1 is a square.
Original entry on oeis.org
7, 10, 24, 26, 65, 13777
Offset: 1
Cf.
A216268 (values of binomial(m, 3)) and
A216269 (square roots of binomial(m, 3) + 1).
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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 *)
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isok(m) = (m>=3) && issquare(binomial(m,3)+1); \\ Michel Marcus, Mar 15 2022
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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
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