A118844 -id:A118844 - cp's OEIS frontend

A118845 Numbers that have non-Brauer chains among their shortest addition chains.

13, 19, 21, 25, 26, 29, 31, 37, 38, 39, 41, 42, 47, 49, 50, 52, 53, 55, 57, 58, 59, 61, 62, 63, 69, 71, 73, 74, 75, 76, 78, 79, 81, 82, 84, 87, 89, 91, 93, 94, 95, 97, 98, 100, 101, 103, 104, 105, 106, 107, 109, 110, 111, 113, 114, 115, 116, 117, 118, 121, 122, 123

Offset: 1

Hugo Pfoertner, May 01 2006

nonn

Indices of nonzero terms in A079302. See A079301 for the definition of a Brauer addition chain.

Giovanni Resta, Tables of Shortest Addition Chains, computed by David W. Wilson.

Cf. A118846 (corresponding counts of minimal non-Brauer chains), A079301 (number of minimal Brauer chains for n), A079302 (number of minimal non-Brauer chains for n), A118844 (numbers without shortest non-Brauer chains).

A118846 Number of non-Brauer chains corresponding to the entries of A118845.

Original entry on oeis.org

1, 2, 3, 1, 2, 18, 13, 6, 5, 2, 3, 6, 37, 1, 2, 3, 34, 17, 25, 44, 4, 15, 32, 7, 3, 244, 7, 13, 2, 8, 6, 129, 3, 6, 9, 73, 77, 69, 45, 90, 13, 1, 2, 3, 49, 15, 4, 46, 81, 4, 25, 44, 13, 20, 62, 3, 73, 7, 9, 20, 35, 7, 52, 4, 20, 674, 3, 3, 6, 163, 403, 673, 124, 8, 15, 2, 20, 6, 157, 11

Offset: 1

Hugo Pfoertner, May 01 2006

nonn

See A079301 for the definition of a Brauer addition chain.

			a(3)=3 because there exist 3 different non-Brauer shortest addition chains for n=A118845(3)=21: [1 2 4 5 8 13 21] and [1 2 4 5 8 16 21] with 8=4+4 (5 not part of sum), [1 2 4 8 9 12 21] with 12=8+4 (9 not part of sum).

Giovanni Resta, Tables of Shortest Addition Chains, computed by David W. Wilson.

Cf. A118845 [numbers with shortest non-Brauer chains], A079301 [Number of minimal Brauer chains for n], A079302 [Number of minimal non-Brauer chains for n], A118844 [numbers without shortest non-Brauer chains].

cp's OEIS Frontend

A118845 Numbers that have non-Brauer chains among their shortest addition chains.

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