A316604 - OEIS

%I #14 Jul 16 2018 04:55:35

%S 11,101,131,133,1013,2111,2619,3173,3301,4111,5907,8463,9101,10033,

%T 10111,12881,13833,14021,14821,15443,16771,17501,17831,18621,21519,

%U 21567,28609,29309,31133,31233,33131,41621,42621,44181,44421,44669,45921,52707,55847,59023

%N Replacing each digit d in decimal expansion of n with d^2 yields a new prime when done recursively three times.

%e 2619 is a term because replacing each digit d by d^2, recursively three times, a prime number is obtained: 2619 -> 436181 (prime); 436181 -> 169361641 (prime); 169361641 -> 13681936136161 (prime).

%e 3173 is a term because replacing each digit d by d^2, recursively three times, a prime number is obtained: 3173 -> 91499 (prime); 91499 -> 811168181 (prime); 811168181 -> 6411136641641 (prime).

%t A316604 = {}; Do[ a=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[n]^2)]]; b=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[a]^2)]]; c=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[b]^2)]]; If[PrimeQ[a] && PrimeQ[b] && PrimeQ[c], AppendTo[A316604,n]], {n,100000}]; A316604

%o (PARI) replace_digits(n) = my(d=digits(n), s=""); for(k=1, #d, s=concat(s, d[k]^2)); eval(s)

%o is(n) = my(x=n, i=0); while(1, x=replace_digits(x); if(!ispseudoprime(x), return(0), i++); if(i==3, return(1))) \\ _Felix Fröhlich_, Jul 08 2018

%Y Cf. A048385, A048388, A048390, A048393.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jul 08 2018