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A068492 Primes that remain prime after each digit is replaced by its square. 5
11, 13, 17, 19, 71, 73, 89, 101, 103, 107, 131, 137, 149, 167, 173, 191, 197, 199, 223, 229, 233, 283, 307, 311, 313, 331, 337, 359, 383, 401, 433, 439, 461, 463, 491, 523, 569, 593, 631, 641, 647, 659, 709, 733, 743, 773, 809, 823, 859, 907, 911, 919, 947 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Zak Seidov, Table of n, a(n) for n = 1..785

EXAMPLE

When each digit of the prime 89 is replaced by its square, 6481, a prime, results. Hence 89 is a term of the sequence.

MATHEMATICA

f[n_] := Block[{a = IntegerDigits[n], b = "", k = 1, l}, l = Length[a]; While[k < l + 1, b = StringJoin[b, ToString[a[[k]]^2]]; k++ ]; ToExpression[b]]; Do[ If[ PrimeQ[ f[ Prime[n]]], Print[ Prime[n]]], {n, 1, 150} ]

PROG

(MAGMA) DigitsSquared:=func< n | StringToInteger(&cat[ IntegerToString(a): a in Reverse([ d^2: d in Intseq(n) ]) ]) >; IsA068492:=func< p | IsPrime(DigitsSquared(p)) >; [ p: p in PrimesUpTo(1000) | IsA068492(p) ]; // Klaus Brockhaus, Mar 05 2011

(PARI)

digsquare(n)={fromdigits(concat(apply(d->if(d, digits(d^2), [0]), digits(n))))}

ok(n)={isprime(n)&&isprime(digsquare(n))} \\ Andrew Howroyd, Feb 27 2018

(Python)

import sympy

n=2

while n>0:

....t=int(''.join([str(int(i)**2) for i in list(str(n))]))

....if sympy.isprime(t)==True:

........print(n)

....n=sympy.nextprime(n)

# Abhiram R Devesh, Feb 09 2015

CROSSREFS

Sequence in context: A132244 A262731 A087201 * A206287 A306661 A045707

Adjacent sequences:  A068489 A068490 A068491 * A068493 A068494 A068495

KEYWORD

base,nonn

AUTHOR

Joseph L. Pe, Mar 11 2002

EXTENSIONS

Edited and extended by Robert G. Wilson v, Mar 19 2002

Duplicate a(1)-a(215) removed from b-file by Andrew Howroyd, Feb 27 2018

STATUS

approved

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)