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

2, 5, 37, 421, 8101, 11771813, 10593030863298469, 17520588382079786917, 644709886888204541861, 126810635974586364597324276501890165253751178116964261, 281339171965861859345972453867311708147087370351598335047820025433137061

Offset

1,1

Links

Table of n, a(n) for n=1..11.

Example

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'.

Prog

(Python)
from sympy import isprime; R = []
for i in range(0, 1000):
    t = 2**i; L = []
    while t not in L: L.append(t); t = (t*t + 1) % 2**(i+1)
    {R.append(j) for j in {L[-1], L[-2]} if j not in R and isprime(j)}
R.sort(); print(*R, sep = ', ')

Crossrefs

Cf. A002522, A066872, A350590.

Sequence in context: A097496 A099657 A107633 * A041959 A051739 A189409

Adjacent sequences: A352970 A352971 A352972 * A352974 A352975 A352976

Keyword

nonn,base

Author

Ya-Ping Lu, Apr 13 2022

Status

approved