A371760 - OEIS

%I #6 Apr 10 2024 09:43:01

%S 33,1093,73,17,97,11,193,17,89,11,193,73,673,13,257,33,41,15,97,65,

%T 1009,13,97,149,190,23,401,41,281,31,133,17,1033,31,89,13,6,59,241,

%U 157,1217,91,145,37,937,29,1289,73,97,41,617,19,137,151,34,103,8641,47,82

%N a(n) is the smallest number k such that the k-th n-gonal number is a Fermat pseudoprime to base 2 (A001567), or -1 if no such number exists.

%C The corresponding pseudoprimes are in A371759.

%H Amiram Eldar, <a href="/A371760/b371760.txt">Table of n, a(n) for n = 3..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PouletNumber.html">Poulet Number</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pseudoprime">Pseudoprime</a>.

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>.

%t p[k_, n_] := ((n - 2)*k^2 - (n - 4)*k)/2; pspQ[n_] := CompositeQ[n] && PowerMod[2, n - 1, n] == 1; a[n_] := Module[{k = 2}, While[! pspQ[p[k, n]], k++]; k]; Array[a, 100, 3]

%o (PARI) p(k, n) = ((n-2)*k^2 - (n-4)*k)/2;

%o ispsp(n) = !isprime(n) && Mod(2, n)^(n-1) == 1;

%o a(n) = {my(k = 2); while(!ispsp(p(k, n)), k++); k;}

%Y Cf. A001567, A293622, A293623, A322130, A321868, A321870, A322123, A322160, A371759.

%K nonn

%O 3,1

%A _Amiram Eldar_, Apr 05 2024