A036944 -id:A036944

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A091920

Smallest n-digit prime with digits from {1,4,7} only, or 0 if no such prime exists.

+10
1

7, 11, 0, 1117, 11117, 0, 1111447, 11111117, 0, 1111111411, 11111111741, 0, 1111111111177, 11111111111411, 0, 1111111111111447, 11111111111111171, 0, 1111111111111111111, 11111111111111111447, 0, 1111111111111111111711

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OFFSET

1,1

COMMENTS

Any 3k-digit number containing only digits from {1,4,7} has a digit-sum divisible by 3. Therefore the number is divisible by 3 and a(3k) = 0 for all positive integers k.

LINKS

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

FORMULA

a(k) <= minimum(A036931(k), A036934(k), A036944(k)), a(3k) = 0 and a(A004023(k)) = (10^A004023(k) - 1)/9 = A004022(k) for all positive integers k. (The inequality above holds iff a(k) contains at least one of each digit 1, 4 and 7.)

MATHEMATICA

Flatten[Table[Select[FromDigits/@Tuples[{1, 4, 7}, n], PrimeQ, 1], {n, 25}]/.{}->{0}] (* Jinyuan Wang, Mar 09 2020 *)

CROSSREFS

Other smallest n-digit primes: A036931 (digits from {1, 4} only), A036934 (digits from {1, 7} only), A036944 (digits from {4, 7} only), A004022 (repunit primes), A004023.

KEYWORD

nonn,base

AUTHOR

Rick L. Shepherd, Feb 12 2004

STATUS

approved

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