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

Author

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

Keywords

• easy
• nonn

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

Examples

			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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
• Rémy Sigrist, PARI program for A124145

Crossrefs

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

Programs

PARI

See Links section.