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 1-3 of 3 results.

A377472 First differences of Colombian or self numbers A003052.

Original entry on oeis.org

2, 2, 2, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 15, 11
Offset: 1

Views

Author

M. F. Hasler, Oct 29 2024

Keywords

Comments

Most terms are equal to 11.
Up to a(103) = 15, the only exceptions are a(n) = 2 for n = 1, 2, 3, 4, 14, 24, ..., 94.
Then a(n) = 2 for n = 112, 122, ..., 192, and a(201) = 15.
Then a(n) = 2 for n = 210, 220, ..., 290, and a(299) = 15.
This pattern repeats 8 times, with a(n) = 15 for n = 397, 495, ..., 887.
Then a(984) = 28, after which the previous pattern resumes, with a(n) = 2 for n = 992, 1002, ..., 1072, then a(n) = 15 for n = 1081, 1179, ..., 1865.
This larger pattern continues with a(n) = 28 for n = 1962, 2940, 3918, ..., 8808.
A still larger pattern starts at a(9785) = 41, after which the previous pattern repeats with a(9881) = 15, later a(10762) = 28 etc.

Links

Crossrefs

Cf. A003052 (Colombian or self numbers), A377473 (range of this sequence), A377474 (indices where new terms appear), A163128, A163139.

Programs

  • PARI
    A377472_upto(N=99)={my(o,L=List()); for(n=1+o=1,oo,if(is_A003052(n), listput(L,n-o); o=n; #L

Formula

a(n) = A003052(n+1) - A003052(n).
a(n) = A163139(n) + 1 = A163128(n+1) - A163128(n) + 1. - Max Alekseyev, Jan 02 2025

A377423 Distinct values of the number of integers between consecutive self numbers (A163139), in order of occurrence.

Original entry on oeis.org

1, 10, 14, 27, 40, 53, 66, 79, 92, 105, 118, 100, 117, 130, 143, 156, 169, 182, 195, 208, 23, 89, 203, 220, 233, 246, 259, 272, 285, 298, 34, 78, 293, 306, 323, 336, 349, 362, 375, 388, 45, 67, 383, 396, 409, 426, 439, 452, 465, 478, 56, 473, 486, 499
Offset: 1

Views

Author

Daniel Mondot, Oct 27 2024

Keywords

Comments

Each new value is typically found between self numbers located around 10^k, for some k.
This sequences exhibits interesting patterns, for instance, many new numbers are 13 apart.

Examples

			Between the first 2 self numbers 1 and 3, there is 1 integer. So 1 is in the sequence
The next new gap is between 9 and 20, with 10 integers, so 10 is in the sequence.
The next new gap is between 1006 and 1021, with 14 integers, so 14 is in the sequence.

Links

Crossrefs

Cf. A003052, A163128, A163139, A225793, A230093, A230094, A377422, A377472, A377473.

Formula

a(n) = A377473(n)-1. - Daniel Mondot, Apr 17 2025

A377474 Indices where new terms arise among first differences of Colombian or self numbers (A377472).

Original entry on oeis.org

1, 5, 103, 984, 9785, 97786, 977787, 9777788, 97777789
Offset: 1

Views

Author

M. F. Hasler, Oct 30 2024

Keywords

Comments

See A377473 for the distinct values of the first differences in the order they appear for the first time.

Examples

			The first value, A377472(1) = 2, appears obviously at index a(1) = 1.
The next three values are the same, but at index a(2) = 5 we have a new, distinct value A377472(5) = 11 = A377423(2).
The next distinct value is A377472(103) = 15 = A377423(3), so a(3) = 103.
Then the next new value is A377472(984) = 28 = A377423(4), so a(4) = 984.
The next new value is A377472(9785) = 41 = A377423(5), so a(5) = 9785.
Then, at n = 97786 = a(6), we have A377472(n) = 54 = A377423(6).
Only at n = 977787 = a(7), we have a new value, A377472(n) = 67 = A377423(7).
At n = 9777788 = a(8), we have the next new value, A377472(n) = 80 = A377423(8).

Crossrefs

Cf. A003052 (Colombian numbers), A377472 (1st differences of Colombian numbers), A377473 (distinct values of A377472 in order of appearance), A377423 (= A377473 - 1).

Programs

  • PARI
    A377473_upto(N=9, show=1)={my(o, c, d, L=List()); for(n=1+o=1, oo, is_A003052(n)||next; c++; if(!setsearch(L, d=n-o), show && printf("%d, ",[c,d]); listput(L,c); #L

Formula

a(n+1) = a(n) + 88*10^(n-1) + 1 for n = 3, 4, ..., 7 at least.

Extensions

a(9) from Daniel Mondot, May 01 2025
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.