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A374029
Lexicographically earliest strictly increasing sequence of prime numbers whose partial products, starting from the second, are all Fermat pseudoprimes to base 2 (A001567).
3
11, 31, 41, 61, 181, 54001, 54721, 61561, 123121, 225721, 246241, 430921, 523261, 800281, 2400841, 9603361, 28810081, 76826881, 96033601, 15909022209601, 133133396385601, 5791302742773601, 15443473980729601, 61773895922918401, 386086849518240001, 13706083157897520001
OFFSET
1,1
COMMENTS
Are all the terms of the form 10*k+1?
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 = NextPrime[a[n-1]], 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++); }
(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(p > P[#P] && isprime(p) && 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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 26 2024
EXTENSIONS
a(20)-a(26) from Daniel Suteu, Jun 30 2024
STATUS
approved