A384735 Numbers that are prime or end in a prime number (of any length).

2, 3, 5, 7, 11, 12, 13, 15, 17, 19, 22, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 42, 43, 45, 47, 52, 53, 55, 57, 59, 61, 62, 63, 65, 67, 71, 72, 73, 75, 77, 79, 82, 83, 85, 87, 89, 92, 93, 95, 97, 101, 102, 103, 105, 107, 109, 111, 112, 113, 115, 117

Offset: 1

Author

Mohd Anwar Jamal Faiz, Jun 08 2025

Keywords

• nonn
• base

Comments

If k is a term, so is m*10^A055642(k) + k for all m > 0. - Michael S. Branicky, Jun 10 2025

Examples

			2, 3, 5, 7 and 11 are terms since they are prime.
15 is a term since it ends in the prime 5.
111 is a term since it ends in the prime 11.
		

Links

• Mohd Anwar Jamal Faiz, Primender Sequence: A Novel Mathematical Construct for Testing Symbolic Inference and AI Reasoning, arXiv:2506.10585 [cs.AI], 2025. See pp. 4, 9.

Crossrefs

Cf. A000040, A033664, A055642.

Contains A017293, A017305, A017329, A017353.

Programs

Maple

q:= n-> isprime(n) or (k-> k>1 and q(n mod 10^(k-1)))(length(n)):
select(q, [$1..150])[];  # Alois P. Heinz, Jun 08 2025

Mathematica

q[n_] := AnyTrue[Range[1, IntegerLength[n]-1], PrimeQ[Mod[n, 10^#]] &]; Select[Range[120], PrimeQ[#] || q[#] &] (* Amiram Eldar, Jun 10 2025 *)

PARI

isok(x) = my(y=x, nb=0); while(y>1, y/=10; nb++; if (isprime(x%(10^nb)), return(1))); \\ Michel Marcus, Jun 10 2025

Python

from sympy import isprime
def ok(n):
    s = str(n)
    return any(isprime(int(s[i:])) for i in range(len(s)))
print([k for k in range(118) if ok(k)])