A036931 Smallest n-digit prime containing only digits 1 and 4, or 0 if no such prime exists.

0, 11, 0, 4111, 11411, 0, 1114111, 11111141, 0, 1111111411, 11111141411, 0, 1111111111441, 11111111111411, 0, 1111111111114441, 11111111111414411, 0, 1111111111111111111, 11111111111111414441, 0, 1111111111111111144141

Offset: 1

Author

Patrick De Geest, Jan 04 1999

Keywords

• nonn
• base

Comments

For any positive integer k, a(3k) = 0 as any 3k-digit number containing only digits 1 or 4 or both has a digit-sum divisible by 3 and thus the number is divisible by 3. - Rick L. Shepherd, Feb 08 2004

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020452, A036304, A036229.

Cf. A004022 (repunit primes), A004023.

Programs

Mathematica

Flatten[Table[Select[FromDigits/@Tuples[{1, 4}, n], PrimeQ, 1], {n, 25}]/.{}->{0}] (* Jinyuan Wang, Mar 09 2020 *)

Formula

a(3k) = 0 and a(A004023(k)) = (10^A004023(k) - 1)/9 = A004022(k) for all positive integers k. - Rick L. Shepherd, Feb 08 2004

Extensions

More terms from Rick L. Shepherd, Feb 08 2004