A383907 Echo primes: primes p such that the greatest prime factor of p-1 is a suffix of p.

13, 73, 127, 163, 193, 197, 313, 337, 419, 433, 757, 929, 1153, 2017, 2311, 2593, 2647, 3137, 3659, 4483, 4673, 5741, 6857, 7057, 12071, 12097, 13267, 13313, 13619, 14407, 15877, 17191, 18041, 18433, 18439, 19273, 19531, 20353, 21319, 21961, 22279, 24103, 24697, 25411

Offset

1,1

Comments

These are primes in A383896(n).

The first pair of twin echo primes is 6467806769 and 6467806771.

Conjecture: There are infinitely many echo primes.

Links

Table of n, a(n) for n=1..44.

Mathematica

Select[Prime@Range@3000, (f=FactorInteger[#-1][[-1, 1]]; Mod[#, 10^IntegerLength@f]==f)&]

Prog

(Python)
from sympy import factorint, isprime
def ok(n): return n > 2 and isprime(n) and str(n).endswith(str(max(factorint(n-1))))
print([k for k in range(30000) if ok(k)]) # Michael S. Branicky, May 15 2025

Crossrefs

Cf. A000040, A006530, A383896.

Sequence in context: A336796 A138353 A097402 * A255416 A201788 A139873

Adjacent sequences: A383904 A383905 A383906 * A383908 A383909 A383910

Keyword

nonn,base

Author

Giorgos Kalogeropoulos, May 15 2025

Status

approved