A346568 Fermat pseudoprimes to base 2 (A001567) k such that A003961(k) is also a Fermat pseudoprime to base 2.

710533, 915981, 1293337, 2134277, 3542533, 13747361, 161216021, 206304961, 284166877, 748419127, 968283247, 1265740717, 2582246701, 4297753027, 10891270501, 11176136947, 11273608417, 11606768801, 12169503061, 13321141597, 14241379237, 17005529227, 19600350001

Offset

1,1

Comments

a(1) = 710533 = 487 * 1459 has 2 distinct prime divisors.

a(2) = 915981 = 3 * 11 * 41 * 677 has 4 distinct prime divisors.

a(58) = 176529862601 = 2141 * 6421 * 12841 is the least term with 3 distinct prime divisors.

a(6884) = 15314196673937701 = 19 * 31 * 41 * 71 * 109 * 281 * 331 * 881 is the least term with 8 distinct prime divisors.

a(111) = 619303584901 is the least term k such that A003961(k) is also a term.

a(30430) = 507728732614597601 is the least term k such that both A003961(k) and A003961(A003961(k)) are also terms.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

710533 = 487 * 1459 is a term since it is a Fermat pseudoprime to base 2, and A003961(710533) = 491 * 1471 = 722261 is also a Fermat pseudoprime to base 2.

Mathematica

psp = Cases[Import["https://oeis.org/A001567/b001567.txt", "Table"], {_, _}][[;; , 2]]; f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; pspQ[n_] := PowerMod[2, n - 1, n] == 1; Select[psp, pspQ[s[#]] &]

Crossrefs

Cf. A001567, A003961.

A346569 is a subsequence.

Sequence in context: A083613 A284166 A083614 * A114675 A234757 A232578

Adjacent sequences: A346565 A346566 A346567 * A346569 A346570 A346571

Keyword

nonn

Author

Amiram Eldar, Jul 23 2021

Status

approved