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A376423
Nonnegative numbers m such that the run lengths in binary expansion of m, say (r_1, ..., r_k), correspond to a complete ruler: the sums r_i + ... r_j with i <= j <= k cover an initial interval of the positive integers.
2
0, 1, 2, 4, 5, 6, 9, 10, 11, 13, 18, 19, 20, 21, 22, 23, 25, 26, 29, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 49, 50, 53, 54, 58, 68, 69, 70, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 98, 101, 102, 105, 106, 109
OFFSET
1,3
COMMENTS
There are A103295(k) terms with k binary digits (ignoring leading zeros).
EXAMPLE
The binary expansion of 35 is "100011", the corresponding run lengths are (1, 3, 2); the sums 1, 2, 3, 1+3, 3+2, 1+3+2 cover the positive integers between 1 and 6, hence 35 is a term.
PROG
(PARI) toruns(n) = { my (r = []); while (n, my (v = valuation(n+n%2, 2)); n \= 2^v; r = concat(v, r)); r }
is(n) = { my (r = toruns(n)); #setbinop((i, j) -> vecsum(r[i..j]), [1..#r])==vecsum(r); }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Sep 22 2024
STATUS
approved