cp's OEIS Frontend

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

%I A270474 #27 Feb 24 2022 15:25:04
%S A270474 2,3,10,11,18,19,42,43,66,67,82,83,106,107,130,131,138,139,162,163,
%T A270474 210,211,282,283,306,307,330,331,346,347,466,467,490,491,498,499,522,
%U A270474 523,546,547,562,563,570,571,586,587,618,619,658,659,690,691,738,739,786,787,810,811,858,859
%N A270474 Integers k such that A256832(k) is not divisible by k*(k+1)/2.
%C A270474 It appears that the odd numbers in the sequence are prime.
%C A270474 This holds at least up to a million. - _Charles R Greathouse IV_, Feb 24 2022
%H A270474 Charles R Greathouse IV, <a href="/A270474/b270474.txt">Table of n, a(n) for n = 1..10000</a>
%e A270474 3 is a term because (1*2*5) is not divisible by (1+2+3).
%t A270474 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 *)
%o A270474 (PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
%o A270474 f(n) = prod(k=1, n, a000129(k)); \\ A256832
%o A270474 for(n=1, 1e3, if(f(n) % (n*(n+1)/2) != 0, print1(n, ", ")));
%o A270474 (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)};
%o A270474 for(k=1,1000,if(k==g(k),print1(g(k)-1,", ",g(k),", "))); \\ _Bill McEachen_, Feb 14 2022 (from A213891 code, faster)
%o A270474 (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
%Y A270474 Cf. A000129, A000217, A213891, A256832.
%K A270474 nonn
%O A270474 1,1
%A A270474 _Altug Alkan_, Mar 17 2016