A117127 -id:A117127 - cp's OEIS frontend

A141439 Positions at which disjoint pattern counts differ from overlapping pattern counts related to sequence A117127.

21, 22, 23, 45, 47, 55, 73, 85, 86, 90, 91, 95, 109, 110, 111, 119, 146, 170, 173, 181, 182, 187, 191, 219, 221, 223, 239, 247, 273, 307, 341, 342, 346, 362, 365, 375, 383, 409, 438, 443, 447, 477, 478, 479, 495, 503, 546, 585, 614, 660, 682, 685, 693, 725

Offset: 1

Diana L. Mecum, Aug 06 2008

			When "n" = 21, the base two concatenated range of integers from 1 to 21 is "1101110010111011110001001101010111100110111101111100001000110010100111010010101". 21 in base two is "10101".
Note that there are two instances of "10101" in the concatenated number when disjoint patterns are considered. There are three pattern matches when overlapping patterns are considered.

Diana Mecum, Table of n, a(n) for n = 1..131

Cf. A117127.

f[n_, k_] := StringCount[ ToString@ FromDigits@ Flatten@ IntegerDigits[ Range@n, 2], ToString@ FromDigits@ IntegerDigits[n, 2], Overlaps -> {True, False}[[k]]]; Select[ Range@ 725, f[ #, 1] != f[ #, 2] &] (* Robert G. Wilson v, Aug 30 2008 *)

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.

Original entry on oeis.org

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

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

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.

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

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

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

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

cp's OEIS Frontend

A141439 Positions at which disjoint pattern counts differ from overlapping pattern counts related to sequence A117127.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica