A293623 - OEIS

%I #11 May 31 2020 02:12:46

%S 7957,241001,1419607,1830985,1993537,2134277,2163001,2491637,2977217,

%T 4864501,5351537,6952037,10084177,11367137,11433301,14609401,21306157,

%U 22591301,26470501,26977001,29581501,35851037,44731051,46517857,53154337,55318957,55610837

%N Fermat pseudoprimes to base 2 that are pentagonal.

%C Rotkiewicz proved that this sequence is infinite.

%C Intersection of A001567 and A000326.

%C The corresponding indices of the pentagonal numbers are 73, 401, 973, 1105, 1153, 1193, 1201, 1289, 1409, 1801, 1889, 2153, 2593, 2753, 2761, ...

%D Andrzej Rotkiewicz, Sur les nombres pseudopremiers pentagonaux, Bull. Soc. Roy. Sci. Liège, Vol. 33 (1964), pp. 261-263.

%H Amiram Eldar, <a href="/A293623/b293623.txt">Table of n, a(n) for n = 1..10000</a>

%e 7957 = (3*73^2 - 73)/2 is in the sequence since it is pentagonal, composite, and 2^7956 == 1 (mod 7957).

%t p[n_]:=(3n^2-n)/2; Select[p[Range[3, 10^4]], PowerMod[2, (# - 1), #]==1 &]

%Y Cf. A000326, A001567.

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 13 2017