A374027 Lexicographically earliest sequence of numbers whose partial products are all Fermat pseudoprimes to base 2 (A001567).

341, 41, 61, 181, 721, 3061, 6121, 9181, 27541, 36721, 91801, 100981, 238681, 21242521, 67665781, 477361, 48690721, 7160401, 76377601, 35802001, 83394792001, 7500519001, 60004152001, 3420236664001, 1380095496001, 13110907212001, 56583915336001, 128003857254001

Offset: 1

Author

Amiram Eldar, Jun 26 2024

Keywords

• nonn

Examples

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

Links

• Daniel Suteu, Table of n, a(n) for n = 1..47
• Index entries for sequences related to pseudoprimes.

Crossrefs

Cf. A001567, A374028, A374029.

Programs

Mathematica

pspQ[n_] := PowerMod[2, n - 1, n] == 1; a[1] = 341; a[n_] := a[n] = Module[{k = 3, r = Product[a[i], {i, 1, n - 1}]}, While[!pspQ[k*r], k+=2]; k]; Array[a, 8]

PARI

ispsp(n) = Mod(2, n)^(n-1) == 1;
lista(len) = {my(prd = 1, c = 0, k = 341); while(c < len, while(!ispsp(prd * k), k += 2); prd *= k; print1(k,", "); c++; k = 3);}

PARI

my(S=List(341),base=2); my(m = vecprod(Vec(S))); my(L = znorder(Mod(base, m))); print1(S[1], ", "); while(1, forstep(k=lift(1/Mod(m, L)), oo, L, if(gcd(m,k) == 1 && k > 1 && base % k != 0, if((m*k-1) % znorder(Mod(base, k)) == 0, print1(k, ", "); listput(S, k); L = lcm(L, znorder(Mod(base, k))); m *= k; break)))); \\ Daniel Suteu, Jun 30 2024

Extensions

a(21)-a(28) from Daniel Suteu, Jun 30 2024