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A352973 Prime numbers p such that iterating the map m -> m^2 + 1 on p generates a number ending with p in binary format.

%I A352973 #6 Jun 04 2022 13:59:10
%S A352973 2,5,37,421,8101,11771813,10593030863298469,17520588382079786917,
%T A352973 644709886888204541861,
%U A352973 126810635974586364597324276501890165253751178116964261,281339171965861859345972453867311708147087370351598335047820025433137061
%N A352973 Prime numbers p such that iterating the map m -> m^2 + 1 on p generates a number ending with p in binary format.
%e A352973 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 A352973 (Python)
%o A352973 from sympy import isprime; R = []
%o A352973 for i in range(0, 1000):
%o A352973     t = 2**i; L = []
%o A352973     while t not in L: L.append(t); t = (t*t + 1) % 2**(i+1)
%o A352973     {R.append(j) for j in {L[-1], L[-2]} if j not in R and isprime(j)}
%o A352973 R.sort(); print(*R, sep = ', ')
%Y A352973 Cf. A002522, A066872, A350590.
%K A352973 nonn,base
%O A352973 1,1
%A A352973 _Ya-Ping Lu_, Apr 13 2022