cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A366826 Composite numbers whose proper substrings (of their decimal expansions) are all primes.

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%I A366826 #19 Nov 19 2023 02:04:52
%S A366826 4,6,8,9,22,25,27,32,33,35,52,55,57,72,75,77,237,537,737
%N A366826 Composite numbers whose proper substrings (of their decimal expansions) are all primes.
%C A366826 There are no terms greater than 999 because the only three-digit prime whose substrings are all primes is 373 (see A085823) and prepending or appending any prime digit to it would create a different three-digit substring.
%e A366826 237 is included because it is composite and 2, 3, 7, 23 and 37 are all primes.
%e A366826 4 is included because it is composite and has no proper substrings.
%o A366826 (Python)
%o A366826 from itertools import combinations
%o A366826 from sympy import isprime
%o A366826 for n in range(2, 1000):
%o A366826     if not isprime(n):
%o A366826         properSubstrings = set(
%o A366826             int(str(n)[start:end]) for (start, end)
%o A366826             in combinations(range(len(str(n)) + 1), 2)
%o A366826         ) - set((n,))
%o A366826         if all(isprime(s) for s in properSubstrings):
%o A366826             print(n, end=', ')
%Y A366826 Subsequence of A002808.
%Y A366826 Cf. A000040.
%Y A366826 Cf. A061371, A062115, A202262.
%Y A366826 Cf. A033274, A068669, A085823, A279366.
%K A366826 base,fini,full,nonn
%O A366826 1,1
%A A366826 _Kalle Siukola_, Oct 25 2023