cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A377911 Indices of the 1's in the digit stream A376771.

Original entry on oeis.org

1, 10, 13, 15, 17, 19, 23, 32, 44, 45, 46, 50, 52, 56, 68, 71, 74, 75, 77, 80, 94, 96, 97, 102, 107, 112, 116, 119, 120, 124, 157, 162, 165, 168, 169, 171, 172, 176, 183, 189, 192, 194, 213, 214, 215, 218, 227, 236, 238, 239
Offset: 1

Views

Author

N. J. A. Sloane, Nov 23 2024

Keywords

Comments

Given that A302656 contains exponentially long runs of 9's, there will be very long gaps in the present sequence.

Crossrefs

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

Views

Author

N. J. A. Sloane, Nov 22 2024

Keywords

Crossrefs

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

A302656 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 digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 109, 18, 10, 17, 19, 89, 100, 27, 26, 36, 199999999999, 11, 16, 20, 15, 12, 24, 199, 45, 54, 63, 72, 81, 90, 108, 117, 126, 135, 29, 79, 299, 69, 39, 101, 13, 289, 144, 22, 14, 23, 31, 33, 21, 25, 110, 35, 1000, 9999999999, 28, 44, 38, 34, 48, 42, 49, 32, 200, 153, 43
Offset: 1

Views

Author

Eric Angelini and Hans Havermann, Apr 11 2018

Keywords

Comments

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.
There are huge jumps in this sequence. For example, here are three consecutive terms: a(96) = 41, a(97) = 2*10^111-1, a(98) = 234.
Records after a(97) are:
a(176) = 2*10^1111-1
a(396) = 2*10^11111-1
a(463) = 2*10^111111-1
a(1918) = 2*10^1111111-1
...
It seems likely that every number will eventually appear (see A376772). After 1262743 terms, according to Dominic McCarty, the smallest missing number is 387 = 9*43. - N. J. A. Sloane, Nov 24 2024
Comment from N. J. A. Sloane, Dec 14 2024 (Start)
Dominic McCarty reports that he has computed 3026560 terms (easy to remember). The only headway he has made is that if any string of digits d1, d2, ..., dn appears in the digit stream with density > 0, then it can be shown that all numbers whose digitsum is the concatenation of d1, d2, ..., dn will eventually appear. (End)
The OEIS contains 16 sequences derived from the present one, none of which seem to have appeared in any other context: see A376769-A376776, A377903-A377904, A377906-A377911.

Examples

			The first nine terms do not change when replaced by their digitsum;
109 = a(10) is replaced by the digitsum 1 + 0 + 9 = 10;
18 = a(11) is replaced by the digitsum 1 + 8 = 9;
10 = a(12) is replaced by the digitsum 1 + 0 = 1;
17 = a(13) is replaced by the digitsum 1 + 7 = 8;
19 = a(14) is replaced by the digitsum 1 + 9 = 10;
89 = a(15) is replaced by the digitsum 8 + 9 = 17;
100 = a(16) is replaced by the digitsum 1 + 0 + 0 = 1;
27 = a(17) is replaced by the digitsum 2 + 7 = 9;
26 = a(18) is replaced by the digitsum 2 + 6 = 8;
36 = a(19) is replaced by the digitsum 3 + 6 = 9;
199999999999 = a(20) is replaced by the digitsum 1 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = 100; etc.
We see that the first and the last column here (the terms of S, which is the present sequence, and S', which is A376769) share the same succession of digits (A376771):
1, 0, 9, 1, 8, 1, 0, 1, 7, 1, 9, 8, 9, 1, 0, 0, 2, 7, 2, 6, 3, 6, 1, 9, 9, 9, 9, ...

Links

Crossrefs

Cf. A007953 (digitsum of n), A376769 (digitsum of a(n)), A376770-A376774.
For records, see A377903 and A377904.
Summary: the 16 sequences derived from the present one are A376769-A376776, A377903-A377904, A377906-A377911.

Extensions

Michael S. Branicky noticed that there were errors in Hans Havermann's data. Following his advice, I deleted Hans's incorrect 2279-term data file and a graph that was based on it. - N. J. A. Sloane, Nov 05 2024.

A376769 a(n) = digitsum of A302656(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 1, 8, 10, 17, 1, 9, 8, 9, 100, 2, 7, 2, 6, 3, 6, 19, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 16, 20, 15, 12, 2, 4, 19, 9, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 90, 10, 8, 11, 7, 12, 6, 13, 5, 2, 9, 7, 9, 2, 9, 9, 6, 9, 3, 9, 10, 11, 3, 2, 8, 9, 14, 4, 22, 14, 23, 3, 13, 3, 21, 25, 1, 10, 3, 5, 1000, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 8, 4
Offset: 1

Views

Author

N. J. A. Sloane, Nov 04 2024

Keywords

Comments

Of course, by the definition of A302656, the present sequence and A302656 have exactly the same sequence of digits (which is now A376771).

Links

Crossrefs

Cf. A007953, A302656, A376770, A376771.
Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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