A068492 Primes that remain prime after each digit is replaced by its square.

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

Offset: 1

Author

Joseph L. Pe, Mar 11 2002

Keywords

• base
• nonn

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..785 from Zak Seidov)

Programs

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

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} ]
Select[Prime[Range[200]],PrimeQ[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]^2)]]]&] (* Harvey P. Dale, Dec 31 2023 *)

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

from sympy import isprime, nextprime
n = 2
while n < 8000:
    t = int(''.join(str(int(i)**2) for i in list(str(n))))
    if isprime(t):
        print(n)
    n = nextprime(n)
# Abhiram R Devesh, Feb 09 2015

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