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A296187
Yarborough primes that remain Yarborough primes when each of their digits are replaced by their squares.
1
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
1,1
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
FORMULA
{A106116(k): A048385(A106116(k)) in A106116}. - Felix Fröhlich, Feb 14 2018
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
Cf. A106116 (Yarborough primes), A048385, A052034, A296563 (digits to cubes).
Sequence in context: A089786 A142894 A141909 * A142517 A158711 A140039
KEYWORD
nonn,base,less
AUTHOR
K. D. Bajpai, Feb 14 2018
STATUS
approved