A247013 Consider the prime factors, with multiplicity, in ascending order, of a composite number not ending in 0. Take their sum and repeat the process deleting the minimum number and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to the reverse of themselves.

4, 9, 14, 94, 194, 371, 1887, 1994, 11282, 25656, 61081, 66691, 112082, 394407, 582225, 4284191, 5681778, 9317913, 9361072, 9493615, 19120874, 75519134, 92688481

Offset

1,1

Comments

Similar to A212875 but reading the sum backwards.

If numbers ending in 0 are allowed, 1200 has factors 2,2,2,2,3,5,5 which add up to 21. - Chai Wah Wu, Sep 12 2014

Links

Table of n, a(n) for n=1..23.

Example

Prime factors of 1994 are 2 and 997;
2 + 997 = 999;
997 + 999 = 1996;
999 + 1996 = 2995;
1996 + 2995 = 4991 that is the reverse of 1994.
Prime factors of 25656 are 2^3, 3 and 1069;
2 + 2 + 2 + 3 + 1069 = 1078;
2 + 2 + 3 + 1069 + 1078 = 2154;
2 + 3 + 1069 + 1078 + 2154 = 4306;
3 + 1069 + 1078 + 2154 + 4306 = 8610;
1069 + 1078 + 2154 + 4306 + 8610 = 17217;
1078 + 2154 + 4306 + 8610 + 17217 = 33365;
2154 + 4306 + 8610 + 17217 + 33365 = 65652 that is the reverse of 25656.

Maple

with(numtheory): R:=proc(w) local x, y; x:=w; y:=0;
while x>0 do y:=10*y+(x mod 10); x:=trunc(x/10); od: y; end:
P:=proc(q, h) local a, b, c, d, j, k, n, t, v; v:=array(1..h);
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2];
b:=nops(a); c:=ilog10(n)+1; t:=0; d:=[];
for k from 1 to b do for j from 1 to a[k, 2] do d:=[op(d), a[k, 1]]; od;
od; d:=sort(d); for k from 1 to nops(d) do v[k]:=d[k]; od; a:=nops(d);
t:=a; t:=t+1; v[t]:=add(v[k], k=1..t-1); if R(v[t])=n then print(n);
else while ilog10(v[t])+1<=c do t:=t+1; v[t]:=add(v[k], k=t-a..t-1);
if R(v[t])=n then print(n); break; fi; od; fi; fi; od; end:
P(10^6, 1000);

Mathematica

A247013 = {};
For[n = 4, n <= 1000000, n++,
 If[Mod[n, 10] == 0 || PrimeQ[n], Continue[]];
 r = IntegerReverse[n];
 a = Flatten[Map[Table[#[[1]], {#[[2]]}] &, FactorInteger[n]]];
 sum = Total[a];
 While[sum < r, sum = Total[a = Join[Rest[a], {sum}]]];
 If[sum == r, AppendTo[A247013, n]];
]; A247013 (* Robert Price, Sep 08 2019 *)

Prog

(Python)
from itertools import chain
from sympy import isprime, factorint
A247013_list = []
for n in range(2, 10**8):
....m = int(str(n)[::-1])
....if n % 10 and not isprime(n):
........x = sorted(chain.from_iterable([p]*e for p, e in factorint(n).items()))
........y = sum(x)
........while y < m:
............x, y = x[1:]+[y], 2*y-x[0]
........if y == m:
............A247013_list.append(n) # Chai Wah Wu, Sep 12 2014

Crossrefs

Cf A097090, A212875, A247012.

Sequence in context: A345407 A105703 A055453 * A122499 A350419 A143709

Adjacent sequences: A247010 A247011 A247012 * A247014 A247015 A247016

Keyword

nonn,more,base

Author

Paolo P. Lava, Sep 09 2014

Extensions

More terms and definition edited by Chai Wah Wu, Sep 12 2014

Status

approved