OFFSET
1,1
COMMENTS
A Yarborough prime is a prime that does not contain digits 0 or 1.
LINKS
Chris C. Caldwell, Yarborough prime
FORMULA
EXAMPLE
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.
MATHEMATICA
k = 2; Select[Prime[Range[1000000]], Min[IntegerDigits[#]] > 1 && Min[IntegerDigits[Flatten[IntegerDigits[(IntegerDigits[#]^k)]]]] > 1 && PrimeQ[FromDigits[Flatten[IntegerDigits[(IntegerDigits[#]^k)]]]] &]
PROG
(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
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
K. D. Bajpai, Feb 14 2018
STATUS
approved