A349636 - OEIS

%I #10 Dec 17 2021 08:58:58

%S 13,31,37,67,79,103,109,151,163,181,193,211,241,367,457,547,571,601,

%T 613,631,709,787,811,1117,1213,1831,2017,2683,3019,3319,3391,3511,

%U 3517,3607,4519,4999,6007,6121,6151,6379,6673,6871,6991,8293,11119,11317,11467

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

%H Martin Ehrenstein, <a href="/A349636/b349636.txt">Table of n, a(n) for n = 1..2004</a>

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

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

%o (Python)

%o from sympy import isprime, primerange

%o def ok(p):

%o     if p < 10: return False

%o     s = str(p)

%o     return all(isprime(int(s[:i] + "1" + s[i:])) for i in range(1, len(s)))

%o def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]

%o print(aupto(12000)) # _Michael S. Branicky_, Nov 23 2021

%Y The terms of A069246 > 10 are a subsequence.

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

%K nonn,base

%O 1,1

%A _Michael S. Branicky_, Nov 23 2021