A374028 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A374028

Lexicographically earliest sequence of prime numbers whose partial products, starting from the second, are all Fermat pseudoprimes to base 2 (A001567).

11, 31, 41, 61, 181, 54001, 6841, 54721, 110017981, 13681, 20521, 61561, 123121, 225721, 246241, 205201, 410401, 1128601, 513001, 3078001, 4617001, 73442619001, 96993612810001, 55404001, 7188669001, 16773561001, 67094244001, 821904489001, 29370505311001

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Daniel Suteu, Table of n, a(n) for n = 1..43

Index entries for sequences related to pseudoprimes.

EXAMPLE

The partial products begin with 11, 11 * 31 = 341 = A001567(1), 11 * 31 * 41 = 13981 = A001567(29), 11 * 31 * 41 * 61 = 852841 = A001567(234), 11 * 31 * 41 * 61 * 181 = 154364221 = A001567(2509), ... .

MATHEMATICA

pspQ[n_] := PowerMod[2, n - 1, n] == 1; a[1] = 11; a[n_] := a[n] = Module[{p = 2, r = Product[a[i], {i, 1, n - 1}]}, While[! pspQ[p*r], p = NextPrime[p]]; p]; Array[a, 10]

PROG

(PARI) ispsp(n) = Mod(2, n)^(n-1) == 1;

lista(len) = {my(prd = 1, c = 0, k = 11); while(c < len, while(!ispsp(prd * k), k = nextprime(k+1)); prd *= k; print1(k, ", "); c++; k = 3); }

(PARI) my(P=List(11), base=2); my(m = vecprod(Vec(P))); my(L = znorder(Mod(base, m))); print1(P[1], ", "); while(1, forstep(p=lift(1/Mod(m, L)), oo, L, if(isprime(p) && m % p != 0 && base % p != 0, if((m*p-1) % znorder(Mod(base, p)) == 0, print1(p, ", "); listput(P, p); L = lcm(L, znorder(Mod(base, p))); m *= p; break)))); \\ Daniel Suteu, Jun 30 2024

CROSSREFS

Cf. A001567, A374027, A374029.

Sequence in context: A240896 A040985 A061599 * A374029 A153128 A040971

Adjacent sequences: A374025 A374026 A374027 * A374029 A374030 A374031

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jun 26 2024

EXTENSIONS

a(23)-a(29) from Daniel Suteu, Jun 30 2024

STATUS

approved