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

%I A349636 #18 Mar 23 2025 23:56:45
%S A349636 13,31,37,67,79,103,109,151,163,181,193,211,241,367,457,547,571,601,
%T A349636 613,631,709,787,811,1117,1213,1831,2017,2683,3019,3319,3391,3511,
%U A349636 3517,3607,4519,4999,6007,6121,6151,6379,6673,6871,6991,8293,11119,11317,11467
%N A349636 Primes that remain prime when a single "1" digit is inserted between any two adjacent digits.
%H A349636 Martin Ehrenstein, <a href="/A349636/b349636.txt">Table of n, a(n) for n = 1..2004</a>
%e A349636 37 and 317 are prime; 2683 is prime, as are 21683, 26183, and 26813.
%t A349636 Select[Prime@Range[5,1500],(p=#;And@@PrimeQ[FromDigits/@(Insert[IntegerDigits@p,1,#]&/@Range[2,IntegerLength@p])])&] (* _Giorgos Kalogeropoulos_, Nov 23 2021 *)
%o A349636 (Python)
%o A349636 from sympy import isprime, primerange
%o A349636 def ok(p):
%o A349636     if p < 10: return False
%o A349636     s = str(p)
%o A349636     return all(isprime(int(s[:i] + "1" + s[i:])) for i in range(1, len(s)))
%o A349636 def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
%o A349636 print(aupto(12000)) # _Michael S. Branicky_, Nov 23 2021
%Y A349636 The terms of A069246 > 10 are a subsequence.
%Y A349636 Cf. A215417 (same with 0), A217044 (2), A217045 (4), A217046 (6), A217047 (8), A217062 (9), A217063 (3), A217064 (5), A217065 (7).
%Y A349636 Subsequence of A002476.
%K A349636 nonn,base
%O A349636 1,1
%A A349636 _Michael S. Branicky_, Nov 23 2021