A296563 Yarborough primes that remain Yarborough primes when each of their digits are replaced by their cubes.

23, 43, 73, 229, 233, 277, 449, 773, 937, 947, 2239, 2243, 2297, 2377, 2777, 3299, 3449, 3727, 3943, 4243, 4423, 4493, 7393, 7723, 7927, 7949, 9227, 9743, 9749, 22277, 22727, 22777, 22943, 23327, 23399, 23497, 23747, 24473, 24733, 27239, 27277, 27427, 27799, 29347

Offset

1,1

Comments

A Yarborough prime is a prime that does not contain digits 0 or 1.

Links

Table of n, a(n) for n=1..44.

Chris C. Caldwell, Yarborough prime

Formula

{A106116(k): A048390(A106116(k)) in A106116} . - R. J. Mathar, May 04 2018

Example

a(1) = 23 is a prime, and replacing each of its digits by its cube yields 827, which is also prime. Neither 23 nor 827 contains digits 0 or 1, so both are Yarborough primes.
a(4) = 229 is a prime, and replacing each of its digits by its cube gives 88729, which is also prime. Neither 229 nor 88729 contains digits 0 or 1, so both are Yarborough primes.
29 is a Yarborough prime but 8729 = 7 * 29 * 43, so 29 is not in the sequence.
53 is a Yarborough prime; 12527 is also a prime but not a Yarborough prime (contains digit 1). Hence, 53 is not included in this sequence.

Mathematica

k = 3; Select[Prime[Range[10000]], Min[IntegerDigits[#]] > 1 && Min[IntegerDigits[Flatten[IntegerDigits[(IntegerDigits[#]^k)]]]] > 1 && PrimeQ[FromDigits[Flatten[IntegerDigits[(IntegerDigits[#]^k)]]]] &]

Crossrefs

Cf. A106116 (Yarborough primes), A296187 (digits to squares), A048390, A277047.

Sequence in context: A281226 A158283 A155786 * A023264 A180534 A138975

Adjacent sequences: A296560 A296561 A296562 * A296564 A296565 A296566

Keyword

nonn,base,less

Author

K. D. Bajpai, Feb 15 2018

Status

approved