A046432 2 steps needed to reach a prime under "Sum of digits raised to its digits' powers" procedure.

3, 69, 96, 123, 132, 203, 213, 222, 230, 231, 302, 312, 320, 321, 334, 343, 433, 447, 456, 465, 469, 474, 477, 496, 546, 564, 566, 577, 645, 649, 654, 656, 665, 689, 694, 698, 744, 747, 757, 774, 775, 777, 869, 896, 946, 964, 968, 986, 1022, 1038, 1048

Offset

1,1

Comments

The sequence is infinite because the numbers of the form m = 111...111 with 10^(p-1) digits, p prime, are terms. - Marius A. Burtea, Oct 27 2019

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1001

Example

a(n)=69 -> 6^6 + 9^9 = 387467145 is composite but 3^3 + 8^8 + 7^7 + 4^4 + 6^6 + 7^7 + 1^1 + 4^4 + 5^5 = 18474623 is prime.

Mathematica

sdp[n_]:=Module[{idn=IntegerDigits[n]/.{0->1}}, Total[#^#&/@idn]]; Select[ Range[ 1100], Rest[PrimeQ[NestList[sdp, #, 2]]]=={False, True}&] (* Harvey P. Dale, Nov 10 2011 *)

Prog

(Magma) f:=func<n| &+[a[i]^a[i]:i in [1..#a]] where a is Intseq(n) >; [k:k in [1..1050] |not IsPrime(f(k)) and IsPrime(f(f(k))) ]; // Marius A. Burtea, Oct 27 2019

Crossrefs

Cf. A046431.

Sequence in context: A279491 A264700 A124181 * A232326 A270869 A241222

Adjacent sequences: A046429 A046430 A046431 * A046433 A046434 A046435

Keyword

nonn,base

Author

Patrick De Geest, Jul 15 1998

Extensions

Offset changed to 1 by Georg Fischer, Oct 27 2019

Status

approved