A270474 Integers k such that A256832(k) is not divisible by k*(k+1)/2.

2, 3, 10, 11, 18, 19, 42, 43, 66, 67, 82, 83, 106, 107, 130, 131, 138, 139, 162, 163, 210, 211, 282, 283, 306, 307, 330, 331, 346, 347, 466, 467, 490, 491, 498, 499, 522, 523, 546, 547, 562, 563, 570, 571, 586, 587, 618, 619, 658, 659, 690, 691, 738, 739, 786, 787, 810, 811, 858, 859

Offset

1,1

Comments

It appears that the odd numbers in the sequence are prime.

This holds at least up to a million. - Charles R Greathouse IV, Feb 24 2022

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

3 is a term because (1*2*5) is not divisible by (1+2+3).

Mathematica

nn = 10^3; Function[k, Select[Range@ nn, ! Divisible[k[[#]], # (# + 1)/2] &]]@ FoldList[Times, LinearRecurrence[{2, 1}, {1, 2}, nn]] (* Michael De Vlieger, Mar 19 2016, after Harvey P. Dale at A256832 *)

Prog

(PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
f(n) = prod(k=1, n, a000129(k)); \\ A256832
for(n=1, 1e3, if(f(n) % (n*(n+1)/2) != 0, print1(n, ", ")));
(PARI) {g(n) = my(t, m=1); if( n<2, 0, while(1, t=contfracpnqn(concat([n, vector(m, i, 2), n])); t=contfrac(n*t[1, 1]/t[2, 1]); if(t[1]<n^2 || t[#t]<n^2, m++, break)); m)};
for(k=1, 1000, if(k==g(k), print1(g(k)-1, ", ", g(k), ", "))); \\ Bill McEachen, Feb 14 2022 (from A213891 code, faster)
(PARI) is(n)=my(m=n^2+n, q=Mod([2, 1; 1, 0], m), Q=q, P=Mod(1, m)); for(k=2, n, P*=(Q*=q)[2, 1]; if(P==0, return(0))); 1 \\ Charles R Greathouse IV, Feb 14 2022

Crossrefs

Cf. A000129, A000217, A213891, A256832.

Sequence in context: A032804 A248407 A047473 * A008509 A281366 A324921

Adjacent sequences: A270471 A270472 A270473 * A270475 A270476 A270477

Keyword

nonn

Author

Altug Alkan, Mar 17 2016

Status

approved