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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.
2
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
1,2
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
CROSSREFS
Sequence in context: A309628 A303716 A309629 * A317706 A302677 A304267
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 25 2002
EXTENSIONS
More terms from Don Reble, Oct 02 2002
Offset corrected by Sean A. Irvine, Feb 26 2025
STATUS
approved