A392622 Lexicographically least increasing sequence of positive integers so that no term is the sum of two consecutive terms, or except for the first term a partial sum of the sequence.

1, 2, 4, 5, 8, 10, 11, 14, 15, 16, 17, 19, 22, 23, 24, 26, 27, 28, 32, 34, 35, 37, 38, 39, 40, 42, 43, 44, 46, 48, 49, 51, 52, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 71, 73, 74, 76, 78, 80, 81, 83, 84, 88, 89, 91, 92, 93, 95, 96, 98, 99, 101, 102, 104

Offset

1,2

Links

Table of n, a(n) for n=1..66.

Example

3 is not a term, since 1 and two are the starting numbers, and 1+2=3.
7 is not a term, since 1+2+4 is 7, with 4 being the next of the smallest numbers.

Mathematica

a[1] = 1; a[2] = 2; a[n_] := a[n] = Module[{k = a[n-1] + 1, s = Join[Total /@ Partition[#, 2, 1], Accumulate[#]]& @ Array[a, n-1]}, While[MemberQ[s, k], k++]; k]; Array[a, 70] (* Amiram Eldar, Jan 18 2026 *)

Crossrefs

Cf. A075326, A249055.

Sequence in context: A324700 A191987 A138007 * A284880 A047261 A286687

Adjacent sequences: A392619 A392620 A392621 * A392623 A392624 A392625

Keyword

nonn

Author

Leo Hennig, Jan 17 2026

Status

approved