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

3,1

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.

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]

Prog

(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; }

Crossrefs

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

Sequence in context: A188989 A189199 A009977 * A293693 A187539 A130835

Adjacent sequences: A371757 A371758 A371759 * A371761 A371762 A371763

Keyword

nonn

Author

Amiram Eldar, Apr 05 2024

Status

approved