A302656 -id:A302656 - cp's OEIS frontend

A376775 a(n) = digitsum of A376773(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 3, 7, 8, 12, 7, 8, 13, 12, 14, 12, 15, 9, 11, 3, 11, 5, 11, 19, 15, 21, 23, 16, 18, 11, 16, 18

Offset: 1

N. J. A. Sloane, Nov 06 2024

Created in the hope (which has not been fulfilled) that it would throw some light on A376773, which are the numbers that take a record time to appear in A302656.

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A377815 Lexicographically earliest infinite sequence of distinct positive integers such that the binary concatenation of its terms yields the same string as the binary concatenation of the binary weights of its terms.

Original entry on oeis.org

1, 5, 2, 3, 4, 8, 15, 255, 7, 11, 13, 14, 16, 19, 21, 22, 6, 25, 32, 9, 26, 63, 65535, 23, 28, 10, 12, 64, 17, 95, 111, 128, 27, 256, 4294967295, 29, 35, 18, 20, 37, 38, 41, 42, 44, 49, 50, 52, 56, 67, 69, 24, 70, 73, 512, 30, 33, 31, 39, 18446744073709551615

Offset: 1

Dominic McCarty, Nov 08 2024

The sequence makes huge jumps. For example, here are three consecutive terms: a(70) = 88, a(71) = 2^256-1, a(72) = 97.
Runs of 0 bits induce large terms since z consecutive 0 bits becomes a term with weight at least 2^z and the smallest such is 2^(2^z) - 1.
The base-2 analog of A302656. The first b terms of this sequence's base-b analog are 1,2,...,(b-1), followed by (b^2+b-1).

			(a(n)):
1,   5,  2,  3,   4,    8,   15,      255,   7, ...
(a(n)) in binary:
1, 101, 10, 11, 100, 1000, 1111, 11111111, 111, ...
Binary weights of (a(n)):
1,   2,  1,  2,   1,    1,    4,        8,   3, ...
Binary weights of (a(n)) in binary:
1,  10,  1, 10,   1,    1,  100,     1000,  11, ...
The two binary lines are the same when concatenated.

Dominic McCarty, Table of n, a(n) for n = 1..451
Dominic McCarty, Log log scatterplot of (n, a(n)) for 1 < n <= 10000
Dominic McCarty, Table of n, a(n), binary weight of a(n) for n = 1..100000

Cf. A302656

A377907 Number of digits in A376769.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2

Offset: 1

N. J. A. Sloane, Nov 22 2024

N. J. A. Sloane, Table of n, a(n) for n = 1..1982

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A377909 a(n) is the unmatched portion of the digit stream A376771 that A303656(n) must match, or -1 if this is the null string.

Original entry on oeis.org

-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 18, 810, 1017, 1719, 1989, 989100, 8910027, 91002726, 100272636, 272636199999999999, 7263619999999999911, 26361999999999991116, 636199999999999111620, 3619999999999911162015, 61999999999991116201512, 199999999999111620151224, 9999999999111620151224199

Offset: 1

N. J. A. Sloane, Nov 22 2024

sign

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A379927 Replacing each term of this sequence S with its digitsum produces a new sequence S' such that S and S' share the same succession of nonzero digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 18, 28, 17, 11, 26, 37, 16, 29, 20, 15, 12, 25, 46, 24, 101, 27, 110, 55, 14, 39, 200, 23, 13, 33, 299, 22, 38, 389, 34, 47, 32, 41, 59, 21, 36, 398, 479, 30, 49, 102, 111, 488, 45, 54, 497, 569, 120, 35, 201, 44, 63, 210, 31

Offset: 1

Rémy Sigrist, Jan 06 2025

The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.

This sequence is a variant of A302656 ignoring zeros; this feature prevents the huge jumps seen in A302656.

			The first terms are:
    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 18, 28, 17, 11, 26, 37, 16, 29, 20
The corresponding digitsums are:
    1, 2, 3, 4, 5, 6, 7, 8, 9, 1,  10, 9,  10, 8,  2,  8,  10, 7,  11, 2
Keeping only the nonzero digits we obtain:
    12345678911918281711263716292
and 123456789119182817112.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A004719, A302656.

PARI
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A377910 a(n) = number of digits in A377909(n), or 0 if A377909(n) = -1.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 4, 4, 6, 7, 8, 9, 18, 19, 20, 21, 22, 23, 24, 25

Offset: 1

N. J. A. Sloane, Nov 22 2024

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

cp's OEIS Frontend

A376775 a(n) = digitsum of A376773(n).

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A377815 Lexicographically earliest infinite sequence of distinct positive integers such that the binary concatenation of its terms yields the same string as the binary concatenation of the binary weights of its terms.

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A377907 Number of digits in A376769.

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Crossrefs

A377909 a(n) is the unmatched portion of the digit stream A376771 that A303656(n) must match, or -1 if this is the null string.

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Author

Keywords

Crossrefs

A379927 Replacing each term of this sequence S with its digitsum produces a new sequence S' such that S and S' share the same succession of nonzero digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A377910 a(n) = number of digits in A377909(n), or 0 if A377909(n) = -1.

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Author

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Crossrefs