A101933 Concatenate the first n positive integers written in binary (with each integer written so the most significant 1 is on the left and the concatenated string is from left to right, A030302). a(n) is the number of times n written in binary appears disjointedly in the concatenated string.

1, 1, 2, 1, 2, 3, 3, 1, 2, 1, 4, 3, 4, 5, 4, 1, 2, 2, 3, 2, 2, 1, 6, 3, 4, 4, 6, 6, 5, 7, 5, 1, 2, 2, 3, 1, 4, 3, 4, 2, 4, 2, 5, 2, 3, 4, 8, 3, 4, 5, 5, 4, 6, 4, 8, 6, 6, 6, 7, 9, 6, 9, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 5, 2, 6, 4, 5, 2, 4, 3, 6, 3, 3, 3, 7, 2, 5, 3, 5, 3, 7, 5, 10, 3, 4, 5, 5, 4, 7, 5, 7, 4, 6

Offset

1,3

Comments

First occurrence of n: 1, 3, 6, 11, 14, 23, 30, 47, 60, 95, 126, 124, 223, 248, 252, 447, 863, 504, 895, 1008, 1020, 1016, 1919, 2044, 2032, 2040, 3839, 7159, 7871, 4080, 7679, 15855, 8160, 8184, 8176, 15839, ??, 16376, 16352, 16368, ..., to a limit of 25000.

Links

Diana Mecum & Robert G. Wilson v, Table of n, a(n) for n = 1..10000.

Example

a(21) = 2 because 21_10 = 10101_2 and that appears in
1101110010111011110001001101010111100110111101111100001000110010100111010010101_2
three times but only two times which do not overlap.

Mathematica

a[n_] := StringCount[ ToString@ FromDigits@ Flatten@ IntegerDigits[ Range@n, 2], ToString@ FromDigits@ IntegerDigits[n, 2], Overlaps -> False]; Array[a, 105]

Crossrefs

Cf. A007088, A030190, A030302, A058935, A047778. Differs from A117127 at positions in A141439.

Sequence in context: A186333 A272917 A239627 * A117127 A278148 A136624

Adjacent sequences: A101930 A101931 A101932 * A101934 A101935 A101936

Keyword

base,easy,nonn

Author

Diana L. Mecum and Robert G. Wilson v, Aug 31 2008

Status

approved