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 A316604 Replacing each digit d in decimal expansion of n with d^2 yields a new prime when done recursively three times. 2
 11, 101, 131, 133, 1013, 2111, 2619, 3173, 3301, 4111, 5907, 8463, 9101, 10033, 10111, 12881, 13833, 14021, 14821, 15443, 16771, 17501, 17831, 18621, 21519, 21567, 28609, 29309, 31133, 31233, 33131, 41621, 42621, 44181, 44421, 44669, 45921, 52707, 55847, 59023 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE 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). 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). MATHEMATICA 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 PROG (PARI) replace_digits(n) = my(d=digits(n), s=""); for(k=1, #d, s=concat(s, d[k]^2)); eval(s) 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 FrÃ¶hlich, Jul 08 2018 CROSSREFS Cf. A048385, A048388, A048390, A048393. Sequence in context: A062696 A113654 A066592 * A208362 A159613 A062332 Adjacent sequences:  A316601 A316602 A316603 * A316605 A316606 A316607 KEYWORD nonn,base AUTHOR K. D. Bajpai, Jul 08 2018 STATUS approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)