A091524 a(m) is the multiplier of sqrt(2) in the constant alpha(m) = a(m)*sqrt(2) - b(m), where alpha(m) is the value of the constant determined by the binary bits in the recurrence associated with the Graham-Pollak sequence.

1, 1, 2, 2, 3, 4, 3, 5, 4, 6, 7, 5, 8, 6, 9, 7, 10, 11, 8, 12, 9, 13, 14, 10, 15, 11, 16, 12, 17, 18, 13, 19, 14, 20, 21, 15, 22, 16, 23, 24, 17, 25, 18, 26, 19, 27, 28, 20, 29, 21, 30, 31, 22, 32, 23, 33, 24, 34, 35, 25, 36, 26, 37, 38, 27, 39, 28, 40, 41, 29, 42, 30, 43, 31, 44

Offset

1,3

Comments

Each integer appears twice. If one deletes the first occurrence of each positive integer one obtains the sequence of positive integers: 1,2,3,4,5,...; i.e., if we enclose in parentheses the first occurrence of 1,2,3,... giving (1),1,(2),2,(3),(4),3,(5),4,(6),(7),5,(8),6,(9),7,(10),... and remove them, we obtain: 1,2,3,4,5,6,7,... The same property holds if one deletes the second occurrence of each positive integer. - Benoit Cloitre, Oct 13 2007

Links

Table of n, a(n) for n=1..75.

Eric Weisstein's World of Mathematics, Graham-Pollak Sequence

Formula

Sequence is completely defined by: a(floor(n*(1+sqrt(2))))=n; a(floor(n*(1+1/sqrt(2))))=n, n>=1 since A003151 and A003152 are Beatty sequences partitioning the integers. - Benoit Cloitre, Oct 13 2007

Conjecture: a(n) = sqrt(A028982(n)/A006337(n)). - Mikhail Kurkov, Apr 25 2024

Example

-1+sqrt(2), -1+sqrt(2), -2+2*sqrt(2), -2+2*sqrt(2), -4+3*sqrt(2), ..., so the sequence of multipliers is 1, 1, 2, 2, 3, ...

Crossrefs

Cf. A001521, A003151, A003152, A006337.

Sequence in context: A300321 A026254 A091525 * A026350 A205002 A370929

Adjacent sequences: A091521 A091522 A091523 * A091525 A091526 A091527

Keyword

nonn

Author

Eric W. Weisstein, Jan 18 2004

Status

approved