A239448 Limiting value of the iterated process of factoring n and concatenating prime powers (in decimal) in the order of increasing primes.

1, 2, 3, 4, 5, 23, 7, 8, 9, 25, 11, 43, 13, 27, 1129, 16, 17, 29, 19, 36389, 37, 211, 23, 83, 25, 3251, 27, 47, 29, 547, 31, 32, 311, 31397, 1129, 49, 37, 373, 313, 3137, 41, 379, 43, 3137, 36389, 223, 47, 163, 49, 71443, 317, 31123, 53, 227, 773, 983, 1129, 229, 59, 3529, 61, 31237, 97, 64, 2719

Offset

1,2

Comments

This is the number reached by iterating the process used in generating A080695, and is similar to the sequence of home primes (A037274), differing by concatenation not of individual primes but, rather, of prime powers. The author suggests using the term 'away number' in a way analogous to 'home prime', thinking that merger of capital 'H' with the symbol '^' suggests capital 'A', etc. (and prime powers--not merely primes--can result, depending on the number). Each positive integral value n should, with heuristic probability 1, have such an away number, and 303 is the first number presenting any challenge finding such (at time of submission). a(1)=1 as a convention, and the numbers that are their own away numbers are the members of A000961.

Links

Table of n, a(n) for n=1..65.

Example

A080695(15)=35, A080695(35)=57, A080695(57)=319, A080695(319)=1129, and A080695(1129)=1129. So, a(15)=1129.

Mathematica

f[n_]:=Module[{l=FactorInteger[n]},
Do[l[[i]]=l[[i, 1]]^l[[i, 2]], {i, 1, Length[l]}];
l=FromDigits[Flatten[IntegerDigits/@l]]];
fp[n_]:=FixedPoint[f, n]; fp/@Range[65] (* Ivan N. Ianakiev, Aug 02 2015 *)

Prog

(PARI)
{
print1(1", "); n=2;
while(1,
  N=n; f=factor(N); m=matsize(f)[1];
  while(m!=1,
    N=f[1, 1]^f[1, 2];
    for(i=2, m,
      e=10; k=f[i, 1]^f[i, 2];
      while(k>e, e*=10); N*=e; N+=k);
    f=factor(N); m=matsize(f)[1]);
  print1(N", "); n++)
}

Crossrefs

Cf. A080695, A037274, A000961.

Sequence in context: A280849 A037400 A080695 * A248713 A242799 A281588

Adjacent sequences: A239445 A239446 A239447 * A239449 A239450 A239451

Keyword

nonn,base

Author

James G. Merickel, Apr 27 2014

Extensions

a(65) corrected by Ivan N. Ianakiev, Aug 02 2015

Status

approved