A392376 Numbers k such that prime(prime(prime(prime(k)))) ends in k.

1, 7, 803, 6061, 38563, 764443, 3727231, 31305459, 40129797, 713413937, 956874279

Offset

1,2

Comments

Numbers k such that A049090(k) ends in k.

Links

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

Formula

a(n) is the set of n >= 1 such that prime(prime(prime(prime(n)))) == n (mod 10^d), where d = length(n).

Example

prime(prime(prime(prime(1)))) = 11,
prime(prime(prime(prime(7)))) = 1787,
prime(prime(prime(prime(803)))) = 11598803,
prime(prime(prime(prime(6061)))) = 204946061,
prime(prime(prime(prime(38563)))) = 2435838563,
prime(prime(prime(prime(764443)))) = 108421764443,
prime(prime(prime(prime(3727231)))) = 759283727231,
prime(prime(prime(prime(31305459)))) = 9836031305459,
prime(prime(prime(prime(40129797)))) = 13218740129797,
prime(prime(prime(prime(713413937)))) = 389697713413937,
prime(prime(prime(prime(956874279)))) = 548264956874279.

Prog

(Python)
from sympy import prime
def P4(n):
    return prime(prime(prime(prime(n))))
limit = 10**9
[n for n in range(1, limit+1) if str(P4(n)).endswith(str(n))]

Crossrefs

Cf. A046883, A049090, A074978, A343128.

Sequence in context: A338968 A342834 A278438 * A279120 A047788 A251698

Adjacent sequences: A392373 A392374 A392375 * A392377 A392378 A392379

Keyword

nonn,base,more

Author

Keiichi Motoi, May 06 2026

Status

approved