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

Author

K. D. Bajpai, Feb 15 2018

Keywords

• nonn
• base
• less

Comments

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

Examples

			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.
		

Links

• Chris C. Caldwell, Yarborough prime

Crossrefs

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

Programs

Mathematica

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

Formula

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