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

1,2

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

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

Mathematica

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

Crossrefs

Cf. A020452, A036304, A036229.

Cf. A004022 (repunit primes), A004023.

Sequence in context: A073864 A277560 A073865 * A165399 A157712 A266379

Adjacent sequences: A036928 A036929 A036930 * A036932 A036933 A036934

Keyword

nonn,base

Author

Patrick De Geest, Jan 04 1999

Extensions

More terms from Rick L. Shepherd, Feb 08 2004

Status

approved