# [seqfan] A sequence closely related to A140525

Peter Pein petsie at dordos.net
Mon Feb 9 13:23:15 CET 2009

```While playing with the function NestList in Mathematica, I found:

vec=NestList[#+1+Cases[FactorInteger[#][[All,1]],_?OddQ,1,1][[1]]&,3,100]

{3,7,15,19,39,43,87,91,99,103,207,211,423,427,435,439,879,883,1767,1771,1779,\
1783,3567,3571,7143,7147,7155,7159,14319,14323,28647,28651,28659,28663,57327,\
57331,114663,114667,114675,114679,229359,229363,229401,229405,229411,229419,\
229423,458847,458851,458979,458983,458991,458995,459001,459523,919047,919051,\
919059,919063,1838127,1838131,3676263,3676267,3676275,3676279,7352559,7352563,\
7352583,7352587,7352599,14705199,14705203,14705293,14707633,29415267,29415271,\
29418819,29418823,29418831,29418835,29418841,58837683,58837687,58838041,\
58838061,58838065,58838071,58838089,117676179,117676183,117677853,117677857,\
117677869,117678919,235357839,235357843,235357851,235357855,235357861,\
235361395,235361401}

which is apparently A140525 + 1.
[to get quick access: http://www.research.att.com/~njas/sequences/A140525 ]

That is:
a(1) = 3,
a(n + 1) = 1 + a(n) + least odd primefactor of a(n)

is there a (simple) proof that this is 1+A140525?

Then it would be worth a comment in A140525, because this definition appears a
bit easier to me than that in A140525.

Cheers,
Peter

```