A054633 -id:A054633 - cp's OEIS frontend

A055074 Pointers to base-2 digits where primes occur in A054633.

3, 4, 5, 7, 8, 9, 12, 17, 19, 20, 21, 22, 29, 30, 33, 39, 47, 49, 64, 65, 71, 72, 76, 77, 83, 91, 102, 103, 106, 113, 114, 115, 120, 122, 129, 142, 155, 156, 157, 173, 174, 175, 179, 180, 185, 186, 193, 194, 197, 198, 203, 204, 225, 233, 245, 249, 264, 265, 267

Offset: 1

Patrick De Geest, Apr 15 2000

			01101110010111011110001001101010111100110111101111...
--|.... sum 0+1+1 = prime 2 at position 3
---|... sum 0+1+1+0 = prime 2 at position 4
----|.. sum 0+1+1+0+1 = prime 3 at position 5
------| sum 0+1+1+0+1+1+1 = prime 5 at position 7

Cf. A000040, A055059-A055073.

A356294 a(n) = A054633(n) if A030190(n) = 1, else a(n) = a(n-A054633(n)+1).

Original entry on oeis.org

1, 2, 1, 3, 4, 5, 2, 1, 6, 3, 7, 8, 9, 4, 10, 11, 12, 13, 5, 2, 1, 14, 6, 3, 15, 16, 7, 17, 8, 18, 9, 19, 20, 21, 22, 4, 10, 23, 24, 11, 25, 26, 27, 28, 12, 29, 30, 31, 32, 33, 13, 5, 2, 1, 34, 14, 6, 3, 35, 36, 15, 16, 37, 7, 38, 17, 8, 39, 40, 41, 18, 42, 9

Offset: 1

Michael De Vlieger and David James Sycamore, Aug 03 2022

Michael De Vlieger, Table of n, a(n) for n = 1..11164
Michael De Vlieger, Log-log scatterplot of a(n), n = 1..2^20, with a color function representing the number k of appearances of m in a(n), where red represents the first appearance of m, and magenta the maximum number of appearances of m in a(1..2^20).

Cf. A030190, A054633.

nn = 120; c =  k = 1; Do[Do[Set[b[k], #[[j]]]; If[b[k] == 1, Set[a[k], c]; c++, Set[a[k], a[k - c + 1]]]; k++, {j, Length[#]}] &@ IntegerDigits[n, 2], {n, nn}]; Array[a[#] &, k - 1] (* Michael De Vlieger, Aug 03 2022 *)

A055143 The first n digits of the juxtaposition of the base-2 numbers converted to decimal.

Original entry on oeis.org

1, 3, 6, 13, 27, 55, 110, 220, 441, 882, 1765, 3531, 7063, 14126, 28253, 56507, 113015, 226031, 452062, 904124, 1808248, 3616497, 7232994, 14465988, 28931977, 57863955, 115727910, 231455821, 462911642, 925823285, 1851646570, 3703293141, 7406586283, 14813172567

Offset: 1

Patrick De Geest, Apr 15 2000

			1 (1); 11 (3); 110 (6); 1101 (13); 11011 (27); 110111 (55); ...

Michael S. Branicky, Table of n, a(n) for n = 1..3322

Cf. A030190, A054633, A055074, A055144-A055150.

With[{c=Flatten[Table[IntegerDigits[n,2],{n,20}]]},Table[FromDigits[ Take[ c,k],2],{k,Length[c]}]] (* Harvey P. Dale, May 15 2021 *)

from itertools import count, islice
def agen():
    k, chap = 1, "1"
    for n in count(1):
        while len(chap) < n: k += 1; chap += bin(k)[2:]
        yield int(chap[:n], 2)
print(list(islice(agen(), 34))) # Michael S. Branicky, Oct 06 2022

a(32) and beyond from Michael S. Branicky, Oct 06 2022

cp's OEIS Frontend

A055074 Pointers to base-2 digits where primes occur in A054633.

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A356294 a(n) = A054633(n) if A030190(n) = 1, else a(n) = a(n-A054633(n)+1).

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A055143 The first n digits of the juxtaposition of the base-2 numbers converted to decimal.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Python

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