A346567 Fermat pseudoprimes to base 2 that are palindromic in base 2.

341, 561, 645, 1105, 2047, 4369, 4681, 5461, 8481, 16705, 33153, 266305, 278545, 526593, 1052929, 1082401, 1398101, 2113665, 2162721, 2290641, 4259905, 6242685, 7674967, 8388607, 16843009, 17895697, 22369621, 34603041, 67371265, 268505089, 280885153, 285212689

Offset: 1

Author

Amiram Eldar, Jul 23 2021

Keywords

• nonn
• base

Comments

There are 133 terms below 2^64. Only 4 of them are also Carmichael numbers (561, 1105, 278545 and 67371265).

Examples

			341 is a term since 341 = 101010101_2 is palindromic in base 2, it is composite (= 11 * 31) and 2^340 == 1 (mod 341).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..133

Crossrefs

Intersection of A001567 and A006995.

A065341 and A281576 are subsequences.

Cf. A016041, A068445.

Programs

Mathematica

pspQ[n_] := CompositeQ[n] && PowerMod[2, n-1, n] == 1; Select[Range[10^6], PalindromeQ[IntegerDigits[#, 2]] && pspQ[#] &]