# [seqfan] Pseudo-arithmetic progressions

Vladimir Shevelev shevelev at bgu.ac.il
Mon Jul 12 16:25:10 CEST 2010

```Dear Seq Fans,

My new submissions are:

%I A179382
%S A179382 1,1,2,1,3,5,6,1,4,9,2,4,10,9,14,5,5,18,10
%N A179382 a(n) is the smallest period of pseudo-arithmetic progression with initial term 1 and difference 2n-1
%C A179382 Let x,y be odd numbers. Denote <+> the following binary operation: x<+>y=A000265(x+y). Let a and d be odd numbers. We call sequence of the form b, b<+>d, (b<+>d)<+>d,... a pdeudo-arithmetic progression with the initial term b and the difference d. It is not difficult to prove that every pdeudo-arithmetic progression is periodic sequence. This sequence lists smallest periods of pseudo-arithmetic progressions with initial term 1 and difference 2n-1, n=1,2,...
%e A179382 For n=5, we have 1<+>9=5, 5<+>9=7, 7<+>9=1. Thus a(5)=3.
%Y A179382 A000265
%K A179382 nonn
%O A179382 1,3

%I A179383
%S A179383 1,5,9,11,13,19,25,29,37
%N A179383 Differences of pseudo-arithmetic progressions with initial term 1 (see A179382) for which the sequence of smallests periods is the sequence of records of A179382
%C A179383 Question. Do exist terms of the sequence having more than 1 prime divisors?
%Y A179383 A139099 A167791 A002326 A179382
%K A179383 nonn
%O A179383 1,2