A349636 Primes that remain prime when a single "1" digit is inserted between any two adjacent digits.

13, 31, 37, 67, 79, 103, 109, 151, 163, 181, 193, 211, 241, 367, 457, 547, 571, 601, 613, 631, 709, 787, 811, 1117, 1213, 1831, 2017, 2683, 3019, 3319, 3391, 3511, 3517, 3607, 4519, 4999, 6007, 6121, 6151, 6379, 6673, 6871, 6991, 8293, 11119, 11317, 11467

Offset

1,1

Links

Martin Ehrenstein, Table of n, a(n) for n = 1..2004

Example

37 and 317 are prime; 2683 is prime, as are 21683, 26183, and 26813.

Mathematica

Select[Prime@Range[5, 1500], (p=#; And@@PrimeQ[FromDigits/@(Insert[IntegerDigits@p, 1, #]&/@Range[2, IntegerLength@p])])&] (* Giorgos Kalogeropoulos, Nov 23 2021 *)

Prog

(Python)
from sympy import isprime, primerange
def ok(p):
    if p < 10: return False
    s = str(p)
    return all(isprime(int(s[:i] + "1" + s[i:])) for i in range(1, len(s)))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(12000)) # Michael S. Branicky, Nov 23 2021

Crossrefs

The terms of A069246 > 10 are a subsequence.

Cf. A215417 (same with 0), A217044 (2), A217045 (4), A217046 (6), A217047 (8), A217062 (9), A217063 (3), A217064 (5), A217065 (7).

Sequence in context: A040086 A176181 A023274 * A129864 A350409 A080387

Adjacent sequences: A349633 A349634 A349635 * A349637 A349638 A349639

Keyword

nonn,base

Author

Michael S. Branicky, Nov 23 2021

Status

approved