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
Offset: 1
Keywords
Examples
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), ... .
Links
Programs
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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] -
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
Extensions
a(23)-a(29) from Daniel Suteu, Jun 30 2024
Comments