A057943 Numbers k such that the smallest palindromic pseudoprime to base k is 101101.

2, 51, 60, 75, 96, 200, 207, 279, 288, 348, 402, 432, 464, 492, 500, 531, 555, 590, 646, 652, 662, 675, 695, 732, 750, 790, 843, 855, 860, 888, 894, 920, 927, 983, 984, 1074, 1102, 1139, 1140, 1150, 1152, 1163, 1164, 1203, 1215, 1230, 1251, 1278, 1283, 1336

Offset: 1

Author

Patrick De Geest, Oct 15 2000

Keywords

• nonn
• base

Examples

			2 is a term since 101101 is the least Fermat pseudoprime to base 2 (A001567) which is also a palindrome in base 10 (A002113).
3 is not a term since the least Fermat pseudoprime to base 3 (A005935) which is also a palindrome in base 10 is 121.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• C. K. Caldwell, Carmichael number
• C. K. Caldwell, Pseudoprimes
• C. Rivera, Carmichael Numbers
• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A001567, A002113, A002997.

Programs

Mathematica

palinComps = Select[Range[2, 101100], PalindromeQ[#] && CompositeQ[#] &]; seqQ[n_] := PowerMod[n, 101100, 101101] == 1 && AllTrue[palinComps, PowerMod[n, #-1, #] != 1 &]; Select[Range[1336], seqQ] (* Amiram Eldar, Jan 30 2020 *)