A124145 a(1)=1, a(2)=2, a(n)=smallest number greater than a(n-1) that can be written as sum of consecutive earlier terms in exactly one way.

1, 2, 3, 5, 6, 8, 10, 16, 17, 18, 19, 22, 25, 26, 29, 32, 33, 37, 40, 41, 43, 45, 47, 48, 50, 54, 55, 57, 59, 62, 66, 67, 68, 69, 73, 75, 76, 77, 81, 83, 85, 86, 87, 95, 98, 99, 101, 105, 109, 117, 118, 120, 126, 128, 129, 131, 133, 134, 137, 139, 140, 141, 143, 146, 148

Offset

1,2

Comments

This sequence is similar to the Hofstadter sequence A005243 except the decomposition into summands has to be unique.

This sequence has similarities with Ulam numbers (A002858); here we consider unique sums of consecutive terms, there unique sums of two distinct terms. - Rémy Sigrist, Jan 02 2022

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Rémy Sigrist, PARI program for A124145

Example

a(7)=10 because 2+3+5=10 is the only way to sum up consecutive terms. 11 is not contained in the sequence because 11=5+6=1+2+3+5 has got more than one decompositions.

Prog

(PARI) See Links section.

Crossrefs

Cf. A002858, A005243, A118065, A118164, A118166.

Sequence in context: A118053 A252482 A348868 * A188064 A104424 A028806

Adjacent sequences: A124142 A124143 A124144 * A124146 A124147 A124148

Keyword

easy,nonn

Author

Tobias Baumann (baumtobi(AT)students.uni-mainz.de), Dec 01 2006

Status

approved