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

1,1

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

Links

Table of n, a(n) for n=1..44.

Chris C. Caldwell, Yarborough prime

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

Adjacent sequences: A296184 A296185 A296186 * A296188 A296189 A296190

Keyword

nonn,base,less

Author

K. D. Bajpai, Feb 14 2018

Status

approved