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A341285
Let B be the set of sequences of positive integers {b(k), k >= 0} such that for some k > 0 (necessarily unique) and any m >= 0, b(m+k) = b(m) + b(m+1) + ... + b(m+k-1); let g(b) = b(0); a(n) is the least value of g(b) for an element b of B containing n.
2
1, 2, 2, 3, 2, 4, 3, 2, 3, 4, 3, 4, 2, 4, 5, 4, 3, 3, 5, 6, 2, 6, 4, 4, 4, 4, 5, 5, 3, 5, 3, 5, 5, 2, 6, 6, 4, 4, 6, 6, 6, 4, 7, 4, 5, 7, 3, 7, 4, 5, 5, 6, 5, 8, 2, 6, 3, 6, 7, 4, 5, 6, 5, 5, 5, 6, 7, 4, 6, 4, 6, 6, 5, 8, 6, 3, 4, 6, 6, 6, 4, 8, 5, 7, 7, 6, 7
OFFSET
1,2
COMMENTS
This sequence is a generalization of A249783 and A341456 to the set of "k-bonacci sequences of positive integers".
LINKS
FORMULA
a(n) <= n.
a(m*n) <= m*a(n).
a(n) = 2 iff n belongs to A020695.
a(n) = A070939(A341699(n)).
EXAMPLE
The first terms of the elements b of B such that g(b) <= 3 are:
g(b) b(0) b(1) b(2) b(3) b(4) b(5) b(6) b(7) b(8) b(9)
---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2
2 1 1 2 3 5 8 13 21 34 55
3 3 3 3 3 3 3 3 3 3 3
3 1 2 3 5 8 13 21 34 55 89
3 2 1 3 4 7 11 18 29 47 76
3 1 1 1 3 5 9 17 31 57 105
- so a(1) = 1,
a(2) = a(3) = a(5) = a(8) = 2,
a(4) = a(7) = a(9) = a(11) = a(17) = a(18) = 3.
PROG
(C) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Feb 16 2021
STATUS
approved