A296187 Yarborough primes that remain Yarborough primes when each of their digits are replaced by their squares.

73, 223, 233, 283, 337, 383, 523, 733, 773, 823, 2333, 2683, 2833, 2857, 3323, 3583, 3673, 3733, 3853, 5333, 6673, 6737, 6883, 7333, 7673, 7727, 7877, 8233, 8563, 8623, 22277, 22283, 22727, 23333, 23833, 25237, 25253, 25633, 26227, 26833, 27583, 27827, 27883, 32257

Offset: 1

Author

K. D. Bajpai, Feb 14 2018

Keywords

• nonn
• base
• less

Comments

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

Terms t of A106116 such that A048385(t) is also a term of A106116. - Felix Fröhlich, Feb 14 2018

Examples

			a(1) = 73 is a prime, and replacing each of its digits by its square yields 499, which is also prime. Neither 73 nor 499 contains digits 0 or 1, so both are Yarborough primes.
a(10) = 823 is a prime, and replacing each of its digits by its square gives 6449, another prime. Neither 823 nor 6449 contains digits 0 or 1, so both are Yarborough primes.
		

Links

• Chris C. Caldwell, Yarborough prime

Crossrefs

Cf. A106116 (Yarborough primes), A048385, A052034, A296563 (digits to cubes).

Programs

Mathematica

k = 2; Select[Prime[Range[1000000]], Min[IntegerDigits[#]] > 1 &&  Min[IntegerDigits[Flatten[IntegerDigits[(IntegerDigits[#]^k)]]]] > 1 && PrimeQ[FromDigits[Flatten[IntegerDigits[(IntegerDigits[#]^k)]]]] &]

PARI

eva(n) = subst(Pol(n), x, 10)
is_a106116(n) = ispseudoprime(n) && vecmin(digits(n)) > 1
a048385(n) = my(d=digits(n), e=[]); for(k=1, #d, d[k]=d[k]^2); for(k=1, #d, my(dd=digits(d[k])); for(t=1, #dd, e=concat(e, dd[t]))); eva(e)
is(n) = is_a106116(n) && is_a106116(a048385(n)) \\ Felix Fröhlich, Mar 26 2018

Formula

{A106116(k): A048385(A106116(k)) in A106116}. - Felix Fröhlich, Feb 14 2018