# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a293623 Showing 1-1 of 1 %I A293623 #11 May 31 2020 02:12:46 %S A293623 7957,241001,1419607,1830985,1993537,2134277,2163001,2491637,2977217, %T A293623 4864501,5351537,6952037,10084177,11367137,11433301,14609401,21306157, %U A293623 22591301,26470501,26977001,29581501,35851037,44731051,46517857,53154337,55318957,55610837 %N A293623 Fermat pseudoprimes to base 2 that are pentagonal. %C A293623 Rotkiewicz proved that this sequence is infinite. %C A293623 Intersection of A001567 and A000326. %C A293623 The corresponding indices of the pentagonal numbers are 73, 401, 973, 1105, 1153, 1193, 1201, 1289, 1409, 1801, 1889, 2153, 2593, 2753, 2761, ... %D A293623 Andrzej Rotkiewicz, Sur les nombres pseudopremiers pentagonaux, Bull. Soc. Roy. Sci. Liège, Vol. 33 (1964), pp. 261-263. %H A293623 Amiram Eldar, Table of n, a(n) for n = 1..10000 %e A293623 7957 = (3*73^2 - 73)/2 is in the sequence since it is pentagonal, composite, and 2^7956 == 1 (mod 7957). %t A293623 p[n_]:=(3n^2-n)/2; Select[p[Range[3, 10^4]], PowerMod[2, (# - 1), #]==1 &] %Y A293623 Cf. A000326, A001567. %K A293623 nonn %O A293623 1,1 %A A293623 _Amiram Eldar_, Oct 13 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE