A349786 Prime numbers p such that iterating the map m -> m^2 on p generates a number ending with p.

5, 41, 61, 241, 281, 401, 521, 601, 641, 761, 881, 1201, 1361, 1601, 2081, 2161, 2801, 3041, 3121, 3361, 3761, 4001, 4241, 4481, 4561, 4721, 4801, 5281, 5441, 5521, 6481, 6961, 7121, 7681, 7841, 8081, 8161, 8641, 9041, 9281, 9521, 9601, 11681, 12161, 12641

Offset: 1

Author

Ya-Ping Lu, Nov 30 2021

Keywords

• nonn
• base

Examples

			41 is a term because iterating the map, m -> m^2, on 41 gives: 41 -> 1681 -> 2825761 -> 7984925229121 -> 63759030914653054346432641, which ends with 41.
		

Crossrefs

Cf. A000290, A348339.

Programs

Mathematica

q[n_] := NestWhileList[Mod[#^2, 10^IntegerLength[n]] &, n, UnsameQ, All][[-1]] == n; Select[Range[10^4], PrimeQ[#] && q[#] &] (* Amiram Eldar, Nov 30 2021 *)

Python

from sympy import nextprime
p0 = 1
while p0 < 13000:
    p = nextprime(p0); s = len(str(p)); t = p; L = set()
    while t not in L: L.add(t); t = (t*t) % 10**s
    if t == p: print(p, end = ', ')
    p0 = p