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A198191
Start with sequence 1,2,3, after this a(n) is smallest number > a(n-1) coprime to sum of previous elements.
1
1, 2, 3, 5, 6, 7, 11, 12, 13, 17, 18, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 41, 43, 44, 45, 47, 52, 53, 59, 60, 61, 67, 68, 71, 73, 74, 75, 77, 78, 79, 81, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98, 100, 101, 103, 104, 105, 107, 109, 111
OFFSET
1,2
COMMENTS
Starting with sequence 1 and adding increasing numbers coprime to sum of previous elements yields periodic sequence A001651.
By starting with 1,2,3, you get this sequence, apparently non-periodic with sporadic periodic runs of varied length.
Sequence appears to have density of about 0.6 with respect to the positive integers.
Not all primes are in this sequence, 19 being the first missing prime.
LINKS
EXAMPLE
1,2,3 are in the sequence by fiat.
The element smaller than 4 are 1,2,3 with sum 6. 4 is not coprime to 6, so 4 is excluded.
The elements smaller than 5 are 1,2,3 with sum 6. 5 is coprime to 6, so 5 is included.
The elements smaller than 6 are 1,2,3,5 with sum 11. 6 is coprime to 11, so 6 is included.
CROSSREFS
Sequence in context: A205523 A343027 A145739 * A243058 A348440 A339267
KEYWORD
nonn
AUTHOR
David W. Wilson, Oct 21 2011
STATUS
approved