A198191 Start with sequence 1,2,3, after this a(n) is smallest number > a(n-1) coprime to sum of previous elements.

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

David W. Wilson, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A198188 A198189 A198190 * A198192 A198193 A198194

Keyword

nonn

Author

David W. Wilson, Oct 21 2011

Status

approved