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

1,1

Links

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

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

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)
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

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