A371760 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.

33, 1093, 73, 17, 97, 11, 193, 17, 89, 11, 193, 73, 673, 13, 257, 33, 41, 15, 97, 65, 1009, 13, 97, 149, 190, 23, 401, 41, 281, 31, 133, 17, 1033, 31, 89, 13, 6, 59, 241, 157, 1217, 91, 145, 37, 937, 29, 1289, 73, 97, 41, 617, 19, 137, 151, 34, 103, 8641, 47, 82

Offset: 3

Author

Amiram Eldar, Apr 05 2024

Keywords

• nonn

Comments

The corresponding pseudoprimes are in A371759.

Links

• Amiram Eldar, Table of n, a(n) for n = 3..10000
• Eric Weisstein's World of Mathematics, Polygonal Number.
• Eric Weisstein's World of Mathematics, Poulet Number.
• Wikipedia, Polygonal number.
• Wikipedia, Pseudoprime.
• Index entries for sequences related to pseudoprimes.

Crossrefs

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

Programs

Mathematica

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]

PARI

p(k, n) = ((n-2)*k^2 - (n-4)*k)/2;
ispsp(n) = !isprime(n) && Mod(2, n)^(n-1) == 1;
a(n) = {my(k = 2); while(!ispsp(p(k, n)), k++); k;}