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

1,1

Links

Table of n, a(n) for n=1..45.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000290, A348339.

Sequence in context: A106963 A276916 A203018 * A199692 A031917 A139846

Adjacent sequences: A349783 A349784 A349785 * A349787 A349788 A349789

Keyword

nonn,base

Author

Ya-Ping Lu, Nov 30 2021

Status

approved