A298757 Numbers k with record value of the least strong pseudoprime to base k (A298756).

2, 1320, 4712, 5628, 7252, 7852, 14787, 17340, 61380, 78750, 254923, 486605, 1804842, 4095086, 12772344, 42162995

Offset: 1

Author

Amiram Eldar, Jan 26 2018

Keywords

• nonn
• more

Comments

The record strong pseudoprimes are 2047, 4097, 4711, 5627, 7251, 7851, 9409, 10261, 11359, 13747, 18299, 25761, 32761, 38323, 40501, 97921, ...

Links

• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A001262, A020229, A020230, A020231, A020232, A020233, A020234, A020235, A298756.

Programs

Mathematica

sppQ[n_?EvenQ, ] := False; sppQ[n?PrimeQ, ] := False; sppQ[n, b_] := Module[{ans=False},s = IntegerExponent[n-1, 2]; d = (n-1)/2^s; If[ PowerMod[b, d, n] == 1, ans=True, Do[If[PowerMod[b, d*2^r, n] == n-1, ans=True], {r, 0, s-1}]];ans]; smallestSPP[b_] := Module[ {k=3}, While[ !sppQ[k,b],k+=2];k ]; sm=0;a={};Do[s=smallestSPP[b];If[s>sm,sm=s;AppendTo[a,b]], {b,2,10^4}];a (* after Jean-François Alcover at A020229 *)

PARI

lista(nn) = {my(m=0); for (n=2, nn, my(r=a298756(n)); if (r>m, m =r; print1(n, ", ")););} \\ Michel Marcus, Jan 31 2022; using pari code in A298756

Extensions

a(9)-a(16) from Jonathan Pappas, Jan 31 2022