cp's OEIS Frontend

A075573 a(1)=1; a(n) is the smallest positive number not occurring earlier, with different parity from a(n-1), such that sum of any subsequence of two or more consecutive terms is composite.

%I A075573 #8 Feb 26 2025 19:09:25
%S A075573 1,8,7,18,15,6,3,36,21,30,9,16,5,44,25,24,27,60,39,42,33,66,69,26,37,
%T A075573 48,57,12,51,14,49,84,63,90,99,120,81,126,29,4,95,22,93,102,129,72,75,
%U A075573 132,111,108,45,96,141,114,105,150,171,54,135,168,123,78,177,144,117
%N A075573 a(1)=1; a(n) is the smallest positive number not occurring earlier, with different parity from a(n-1), such that sum of any subsequence of two or more consecutive terms is composite.
%C A075573 The sequence is infinite. To extend it from the first N terms, one seeks a constellation of composite numbers, of the right parity, whose span is no greater than the sum of the first N terms, S(N). There are infinitely many sequences, of consecutive composite numbers, of length S(N)+1 (indeed, any particular length); and each of those contains a sequence of length S(N) with the right parity. One of those must suffice and that puts an upper-bound on the N+1'st term. - _Don Reble_, Oct 02 2002
%H A075573 Sean A. Irvine, <a href="/A075573/b075573.txt">Table of n, a(n) for n = 1..1000</a>
%K A075573 nonn
%O A075573 1,2
%A A075573 _Amarnath Murthy_, Sep 25 2002
%E A075573 More terms from _Don Reble_, Oct 02 2002
%E A075573 Offset corrected by _Sean A. Irvine_, Feb 26 2025