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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 09:13 EDT 2022. Contains 357140 sequences. (Running on oeis4.)