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A069490 Primes > 1000 in which every substring of lengths 2 and 3 are also prime.

%I A069490 #14 Jul 02 2021 16:33:17
%S A069490 1373,3137,3797,6131,6173,6197,9719,11311,11317,17971,31379,61379,
%T A069490 71971,113131,113173,113797,131311,131317,131797,179719,317971,431311,
%U A069490 431797,617971,1131131,1131379,1311311,1313797,1317971,3131137,3131311
%N A069490 Primes > 1000 in which every substring of lengths 2 and 3 are also prime.
%C A069490 For all terms: substrings of length 3 correspond to one of the first 21 terms of A069489. - _Reinhard Zumkeller_, Jun 08 2015
%H A069490 Reinhard Zumkeller, <a href="/A069490/b069490.txt">Table of n, a(n) for n = 1..100</a>
%e A069490 11317 is a term as the substrings of length 2, i.e., 11, 13, 31, 17 and the three substrings of length 3, i.e., 113, 131 and 317 are all prime.
%t A069490 Do[ If[ Union[ PrimeQ[ Map[ FromDigits, Partition[ IntegerDigits[ Prime[n]], 2, 1]]]] == Union[ PrimeQ[ Map[ FromDigits, Partition[ IntegerDigits[ Prime[n]], 3, 1]]]] == {True}, Print[ Prime[n]]], {n, PrimePi[1000] + 1, 10^5}]
%t A069490  Select[Prime[Range[169,226000]],AllTrue[FromDigits/@Flatten[Table[ Partition[ IntegerDigits[ #],k,1],{k,{2,3}}],1],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 02 2021 *)
%o A069490 (Haskell)
%o A069490 import Data.Set (fromList, deleteFindMin, union)
%o A069490 a069490 n = a069490_list !! (n-1)
%o A069490 a069490_list = f $ fromList [1..9] where
%o A069490    f s | m < 1000               = f s''
%o A069490        | h m && a010051' m == 1 = m : f s''
%o A069490        | otherwise              = f s''
%o A069490        where s'' = union s' $ fromList $ map (+ (m * 10)) [1, 3, 7, 9]
%o A069490              (m, s') = deleteFindMin s
%o A069490    h x = x < 100 && a010051' x == 1 ||
%o A069490          a010051' (x `mod` 1000) == 1 &&
%o A069490          a010051' (x `mod` 100) == 1 && h (x `div` 10)
%o A069490 -- _Reinhard Zumkeller_, Jun 08 2015
%Y A069490 Cf. A069488 and A069489.
%Y A069490 Cf. A010051, A038618.
%K A069490 nonn
%O A069490 1,1
%A A069490 _Amarnath Murthy_, Mar 30 2002
%E A069490 Edited, corrected and extended by _Robert G. Wilson v_, Apr 12 2002