cp's OEIS Frontend

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

%I A239448 #18 Aug 03 2015 04:22:13
%S A239448 1,2,3,4,5,23,7,8,9,25,11,43,13,27,1129,16,17,29,19,36389,37,211,23,
%T A239448 83,25,3251,27,47,29,547,31,32,311,31397,1129,49,37,373,313,3137,41,
%U A239448 379,43,3137,36389,223,47,163,49,71443,317,31123,53,227,773,983,1129,229,59,3529,61,31237,97,64,2719
%N A239448 Limiting value of the iterated process of factoring n and concatenating prime powers (in decimal) in the order of increasing primes.
%C A239448 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.
%e A239448 A080695(15)=35, A080695(35)=57, A080695(57)=319, A080695(319)=1129, and A080695(1129)=1129. So, a(15)=1129.
%t A239448 f[n_]:=Module[{l=FactorInteger[n]},
%t A239448 Do[l[[i]]=l[[i,1]]^l[[i,2]],{i,1,Length[l]}];
%t A239448 l=FromDigits[Flatten[IntegerDigits/@l]]];
%t A239448 fp[n_]:=FixedPoint[f,n];fp/@Range[65] (* _Ivan N. Ianakiev_, Aug 02 2015 *)
%o A239448 (PARI)
%o A239448 {
%o A239448 print1(1", ");n=2;
%o A239448 while(1,
%o A239448   N=n;f=factor(N);m=matsize(f)[1];
%o A239448   while(m!=1,
%o A239448     N=f[1,1]^f[1,2];
%o A239448     for(i=2,m,
%o A239448       e=10;k=f[i,1]^f[i,2];
%o A239448       while(k>e,e*=10);N*=e;N+=k);
%o A239448     f=factor(N);m=matsize(f)[1]);
%o A239448   print1(N", ");n++)
%o A239448 }
%Y A239448 Cf. A080695, A037274, A000961.
%K A239448 nonn,base
%O A239448 1,2
%A A239448 _James G. Merickel_, Apr 27 2014
%E A239448 a(65) corrected by _Ivan N. Ianakiev_, Aug 02 2015