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%I #24 Apr 03 2023 10:36:13
%S 73,223,233,283,337,383,523,733,773,823,2333,2683,2833,2857,3323,3583,
%T 3673,3733,3853,5333,6673,6737,6883,7333,7673,7727,7877,8233,8563,
%U 8623,22277,22283,22727,23333,23833,25237,25253,25633,26227,26833,27583,27827,27883,32257
%N Yarborough primes that remain Yarborough primes when each of their digits are replaced by their squares.
%C A Yarborough prime is a prime that does not contain digits 0 or 1.
%C Terms t of A106116 such that A048385(t) is also a term of A106116. - _Felix Fröhlich_, Feb 14 2018
%H Chris C. Caldwell, <a href="https://t5k.org/glossary/xpage/YarboroughPrime.html">Yarborough prime</a>
%F {A106116(k): A048385(A106116(k)) in A106116}. - _Felix Fröhlich_, Feb 14 2018
%e 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.
%e 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.
%t k = 2; Select[Prime[Range[1000000]], Min[IntegerDigits[#]] > 1 && Min[IntegerDigits[Flatten[IntegerDigits[(IntegerDigits[#]^k)]]]] > 1 && PrimeQ[FromDigits[Flatten[IntegerDigits[(IntegerDigits[#]^k)]]]] &]
%o (PARI) eva(n) = subst(Pol(n), x, 10)
%o is_a106116(n) = ispseudoprime(n) && vecmin(digits(n)) > 1
%o 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)
%o is(n) = is_a106116(n) && is_a106116(a048385(n)) \\ _Felix Fröhlich_, Mar 26 2018
%Y Cf. A106116 (Yarborough primes), A048385, A052034, A296563 (digits to cubes).
%K nonn,base,less
%O 1,1
%A _K. D. Bajpai_, Feb 14 2018
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