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A004762
Numbers whose binary expansion does not begin 100.
1
0, 1, 2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98
OFFSET
1,3
FORMULA
a(n+1) = n + 2^A099396(n).
G.f.: x/(1-x)^2 + x/(1-x) * Sum[k>=0, 2^k*x^(3*2^k)].
a(1) = 0, a(2) = 1, a(3) = 2, a(4) = 3, a(2^(m+1) + 2^m + k + 2) = 2^(m+2) + 2^m + k, m >= 0, 0 <= k < (2^(m+1) + 2^m). - Yosu Yurramendi, Aug 08 2016
MATHEMATICA
Join[{0, 1, 2, 3}, Select[Range[4, 100], Take[IntegerDigits[#, 2], 3]!={1, 0, 0}&]] (* Harvey P. Dale, Feb 02 2015 *)
CROSSREFS
Complementary to A004756.
Cf. A099396.
Sequence in context: A349019 A225354 A166111 * A061854 A373376 A367861
KEYWORD
nonn,easy,base
STATUS
approved