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.

A376773 Records in A376772.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 21, 25, 44, 48, 52, 53, 58, 75, 77, 84, 96, 135, 146, 300, 317, 401, 452, 478, 1608, 1677, 1679, 1681, 1683, 1703, 1753, 1773, 13649, 13704, 124912, 124925, 125336, 128212, 128221, 128347, 128376, 128529
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2024 (with thanks to Michael S. Branicky)

Keywords

Comments

Numbers that are the slowest to appear in A302656.

Crossrefs

Cf. A302656, A376772, A376774, A376775.
Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

Extensions

a(37)-a(46) from Dominic McCarty, Nov 08 2024

A376774 Indices of records in A376772.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 21, 25, 28, 30, 37, 40, 41, 50, 55, 57, 66, 67, 76, 85, 93, 94, 139, 148, 157, 165, 174, 175, 179, 188, 197, 269, 278, 279, 288, 297, 369, 378
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2024 (with thanks to Michael S. Branicky)

Keywords

Crossrefs

Cf. A302656, A376772, A376773.
Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

Extensions

a(37)-a(46) from Dominic McCarty, Nov 08 2024

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.

A376776 Position of prime(n) in A302656, or -1 if prime(n) does not appear in A302656.

Original entry on oeis.org

2, 3, 5, 7, 21, 44, 13, 14, 49, 38, 50, 77, 96, 68, 78, 81, 83, 138, 401, 113, 149, 39, 181, 15, 1646, 43, 110, 161, 10, 153, 364, 162, 432, 1679, 471, 451, 1683, 425, 1691, 1615, 13649
Offset: 1

Views

Author

N. J. A. Sloane, Nov 06 2024

Keywords

Comments

The primes in A302656 do not appear in their natural order.

Examples

			Prime(5) = 11, and A302656(21) = 11, so a(5) = 11.
Prime(40) = 173, and A302656(1615) = 173, so a(40) = 1615.

Crossrefs

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

Extensions

a(41) = 13649 from Dominic McCarty's b-file for A376772 added by N. J. A. Sloane, Nov 21 2024
Showing 1-4 of 4 results.

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

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