A068492 - OEIS

%I #34 Dec 31 2023 12:16:35

%S 11,13,17,19,71,73,89,101,103,107,131,137,149,167,173,191,197,199,223,

%T 229,233,283,307,311,313,331,337,359,383,401,433,439,461,463,491,523,

%U 569,593,631,641,647,659,709,733,743,773,809,823,859,907,911,919,947

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

%H Chai Wah Wu, <a href="/A068492/b068492.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..785 from Zak Seidov)

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

%t 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} ]

%t Select[Prime[Range[200]],PrimeQ[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]^2)]]]&] (* _Harvey P. Dale_, Dec 31 2023 *)

%o (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

%o (PARI)

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

%o ok(n)={isprime(n)&&isprime(digsquare(n))} \\ _Andrew Howroyd_, Feb 27 2018

%o (Python)

%o from sympy import isprime, nextprime

%o n = 2

%o while n < 8000:

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

%o     if isprime(t):

%o         print(n)

%o     n = nextprime(n)

%o # _Abhiram R Devesh_, Feb 09 2015

%K base,nonn

%O 1,1

%A _Joseph L. Pe_, Mar 11 2002

%E Edited and extended by _Robert G. Wilson v_, Mar 19 2002

%E Duplicate a(1)-a(215) removed from b-file by _Andrew Howroyd_, Feb 27 2018