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A378563 Primes that remain prime if any three of their digits are deleted.

%I A378563 #21 Dec 03 2024 12:49:39
%S A378563 2237,2273,2333,2357,2377,2557,2753,2777,3253,3257,3323,3373,3527,
%T A378563 3533,3557,3727,3733,5227,5233,5237,5273,5323,5333,5527,5557,5573,
%U A378563 5737,7237,7253,7333,7523,7537,7573,7577,7723,7727,7753,7757,11113,11117,11119,11131,11171,11173,11197
%N A378563 Primes that remain prime if any three of their digits are deleted.
%C A378563 Any 4-digit term has all digits prime (cf. A019546).
%C A378563 The corresponding sequence for two digits deleted contains only 18 terms up to 10^100 (Cf. A378081).
%C A378563 Any term >= 10000 must have its last four digits be from {1, 3, 7, 9}. - _Michael S. Branicky_, Dec 01 2024
%e A378563 43117 is in the sequence since upon deleting any three digits we get 43, 31, 11, 17 and 47, all of which are prime.
%o A378563 (Python)
%o A378563 from sympy import isprime
%o A378563 from itertools import combinations as C
%o A378563 def ok(n):
%o A378563     if n < 1000 or not isprime(n): return False
%o A378563     s = str(n)
%o A378563     return all(isprime(int(t)) for i, j, k in C(range(len(s)), 3) if (t:=s[:i]+s[i+1:j]+s[j+1:k]+s[k+1:])!="")
%o A378563 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Dec 01 2024
%Y A378563 Cf. A019546, A051362, A378081.
%K A378563 nonn,base,less
%O A378563 1,1
%A A378563 _Enrique Navarrete_, Nov 30 2024