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A316982 Numbers n such that replacing each digit d in the decimal expansion of n with d^3 yields a prime each time, when done recursively three times. 1
11, 31, 101, 173, 1307, 1873, 10111, 11923, 12209, 14767, 20357, 20729, 21149, 22003, 22151, 29261, 43681, 43891, 52033, 52211, 55231, 58121, 65011, 70027, 70399, 80569, 100087, 101111, 101401, 102079, 102113, 120091, 151931, 163669, 172001, 200501, 201113, 203831 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..235 (* Terms up to 2500000. *)

EXAMPLE

173 is a term because replacing each digit d by d^3, recursively three times, a prime number is obtained: 173 -> 134327 (prime); 134327 -> 12764278343 (prime); 12764278343 -> 18343216648343512276427 (prime).

1873 is a term because replacing each digit d by d^3, recursively three times, a prime number is obtained: 1873 -> 151234327 (prime); 151234327 -> 1125182764278343 (prime); 1125182764278343 -> 11812515128343216648343512276427 (prime).

MATHEMATICA

A316982 = {}; Do[a=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[n]^3)]]; b=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[a]^3)]]; c=FromDigits[Flatten[IntegerDigits /@ (IntegerDigits[b]^3)]]; If[PrimeQ[a] && PrimeQ[b] && PrimeQ[c], AppendTo[A316982, n]], {n, 300000}]; A316982 (* or *)

c[n_] := FromDigits@ Flatten@ IntegerDigits[IntegerDigits[n]^3]; Select[Range[204000], PrimeQ[x = c@#] && PrimeQ[y = c@x] && PrimeQ@c@y &] (* Giovanni Resta, Jul 18 2018 *)

p3[n_]:=Rest[NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]^3)]]&, n, 3]]; Select[Range[205000], AllTrue[p3[#], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 11 2019 *)

PROG

(PARI) eva(n) = subst(Pol(n), x, 10)

replace_digits(n) = my(d=digits(n), e=[]); for(x=1, #d, my(f=digits(d[x]^3)); if(f==[], e=concat(e, [0]), for(y=1, #f, e=concat(e, f[y])))); eva(e)

is(n) = my(x=n, i=0); while(i < 3, x=replace_digits(x); if(!ispseudoprime(x), break, i++)); i >= 3 \\ Felix Fröhlich, Oct 24 2018

CROSSREFS

Cf. A048385, A048390, A048393, A316604.

A004022 is a subsequence.

Sequence in context: A299782 A027847 A068841 * A192246 A124296 A223388

Adjacent sequences:  A316979 A316980 A316981 * A316983 A316984 A316985

KEYWORD

nonn,base

AUTHOR

K. D. Bajpai, Jul 18 2018

STATUS

approved

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Last modified July 4 12:18 EDT 2020. Contains 335448 sequences. (Running on oeis4.)