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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 15 15:31 EDT 2022. Contains 356148 sequences. (Running on oeis4.)