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.

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, 48, 57, 12, 51, 14, 49, 84, 63, 90, 99, 120, 81, 126, 29, 4, 95, 22, 93, 102, 129, 72, 75, 132, 111, 108, 45, 96, 141, 114, 105, 150, 171, 54, 135, 168, 123, 78, 177, 144, 117

Offset: 1

Author

Amarnath Murthy, Sep 25 2002

Keywords

• nonn

Comments

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

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1000

Extensions

More terms from Don Reble, Oct 02 2002

Offset corrected by Sean A. Irvine, Feb 26 2025