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%I #12 Dec 03 2024 12:48:52
%S 222,225,232,235,237,252,253,255,272,273,275,322,323,325,327,332,333,
%T 335,352,355,357,372,375,377,522,525,527,532,533,535,537,552,553,555,
%U 572,573,575,722,723,725,732,735,737,752,753,755,772,775,777,1111,1113,1119,1131,1137,1173,1179,1197,1311,1317,1371
%N Composites that become prime when any two of their digits are deleted.
%C Any term < 1000 has exactly three digits and all digits are prime (cf. A061371).
%C The repunits (cf. A002275) R_21, R_25, R_319, R_1033 and R_49083, among others, are in the sequence since R_19, R_23, R_317, R_1031 and R_49081 are prime (cf. A004023).
%C The corresponding sequence for primes (cf. A378081) contains only 18 terms up to 10^100.
%e 1371 is in the sequence since upon deleting any two digits we get 13, 71, 17, 31, 11 and 37, all of which are prime.
%e 1313 is not in the sequence since upon deleting the two 1s we get 33, which is not prime.
%t q[n_] := Module[{d = IntegerDigits[n]}, AllTrue[FromDigits /@ Subsets[d, {Length[d] - 2}], PrimeQ]]; Select[Range[100, 1500], CompositeQ[#] && q[#] &] (* _Amiram Eldar_, Nov 26 2024 *)
%o (Python)
%o from sympy import isprime
%o from itertools import combinations as C
%o def ok(n):
%o if n < 100 or isprime(n): return False
%o s = str(n)
%o return all(isprime(int(t)) for i, j in C(range(len(s)), 2) if (t:=s[:i]+s[i+1:j]+s[j+1:])!="")
%o print([k for k in range(1500) if ok(k)]) # _Michael S. Branicky_, Nov 26 2024
%Y Cf. A002808, A002275, A004023, A061371, A378081.
%K nonn,base
%O 1,1
%A _Enrique Navarrete_, Nov 26 2024