A352973 - OEIS

%I #6 Jun 04 2022 13:59:10

%S 2,5,37,421,8101,11771813,10593030863298469,17520588382079786917,

%T 644709886888204541861,

%U 126810635974586364597324276501890165253751178116964261,281339171965861859345972453867311708147087370351598335047820025433137061

%N Prime numbers p such that iterating the map m -> m^2 + 1 on p generates a number ending with p in binary format.

%e 37 is a term because iterating the map on 37, which is '100101' in binary format, gives: 37 -> 1370 -> 1876901, which in binary format is '111001010001110100101' ending with '100101'.

%o (Python)

%o from sympy import isprime; R = []

%o for i in range(0, 1000):

%o     t = 2**i; L = []

%o     while t not in L: L.append(t); t = (t*t + 1) % 2**(i+1)

%o     {R.append(j) for j in {L[-1], L[-2]} if j not in R and isprime(j)}

%o R.sort(); print(*R, sep = ', ')

%Y Cf. A002522, A066872, A350590.

%K nonn,base

%O 1,1

%A _Ya-Ping Lu_, Apr 13 2022