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.

A308727 Lexicographically earliest sequence of distinct terms such that the digits of two contiguous terms sum up to a square.

Original entry on oeis.org

1, 3, 6, 12, 10, 8, 17, 26, 35, 44, 53, 62, 71, 80, 89, 107, 98, 116, 100, 21, 15, 19, 24, 28, 33, 30, 42, 37, 51, 46, 60, 55, 69, 64, 78, 73, 87, 82, 96, 91, 105, 102, 49, 39, 4, 5, 13, 14, 22, 23, 29, 32, 31, 41, 38, 50, 40, 48, 58, 57, 67, 66, 76, 75, 85, 84, 94, 93, 103, 104, 47, 59, 2, 7, 9, 16, 11, 20, 25, 18, 34, 27, 43, 36, 52
Offset: 1

Views

Author

Jean-Marc Falcoz and Eric Angelini, Jun 20 2019

Keywords

Comments

It is conjectured that this sequence is a permutation of the integers > 0.

Examples

			The sequence starts with 1,3,6,12,10,8,17,26,... and we see indeed that the digits of:
{a(1); a(2)} have sum 1 + 3 = 4 (square);
{a(2); a(3)} have sum 3 + 6 = 9 (square);
{a(3); a(4)} have sum 6 + 1 + 2 = 9 (square);
{a(4); a(5)} have sum 1 + 2 + 1 + 0 = 4 (square);
{a(5); a(6)} have sum 8 + 1 + 7 = 16 (square);
{a(6); a(7)} have sum 1 + 7 + 2 + 6 = 16 (square);
etc.

Links

Crossrefs

Cf. A308719 (same idea with palindromes instead of squares).

A308728 Lexicographically earliest sequence of distinct terms such that the digits of two contiguous terms sum up to a prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 5, 8, 9, 11, 10, 13, 12, 17, 14, 15, 16, 19, 18, 20, 21, 22, 25, 24, 23, 26, 27, 28, 30, 31, 34, 33, 29, 35, 32, 39, 38, 42, 41, 44, 36, 37, 43, 40, 45, 46, 49, 51, 47, 48, 50, 53, 54, 55, 52, 57, 56, 60, 58, 64, 61, 66, 65, 62, 63, 59, 69, 68, 72, 71, 74, 75, 70, 73, 67, 79, 76, 82, 81, 77, 78, 80, 83
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Jun 20 2019

Keywords

Comments

It is conjectured that this sequence is a permutation of the integers > 0.

Examples

			The sequence starts with 1,2,3,4,7,6,5,8,9,11,10,13,... and we see indeed that the digits of:
{a(1); a(2)} have sum 1 + 2 = 3 (prime);
{a(2); a(3)} have sum 2 + 3 = 5 (prime);
{a(3); a(4)} have sum 3 + 4 = 7 (prime);
{a(4); a(5)} have sum 4 + 7 = 11 (prime);
{a(5); a(6)} have sum 7 + 6 = 13 (prime);
{a(6); a(7)} have sum 6 + 5 = 11 (prime);
{a(7); a(8)} have sum 5 + 8 = 13 (prime);
{a(8); a(9)} have sum 8 + 9 = 17 (prime);
{a(9); a(10)} have sum 9 + 1 + 1 = 11 (prime);
{a(10); a(11)} have sum 1 + 1 + 1 + 0 = 3 (prime);
{a(11); a(12)} have sum 1 + 0 + 1 + 3 = 5 (prime);
etc.

Links

Crossrefs

Cf. A308719 (same idea with palindromes) and A308727 (with squares).

A326315 Lexicographically earliest sequence of distinct terms such that the digits of a(n) and a(n+1) sum up to a palindrome and a(n) + a(n+1) is also a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 196, 197, 277, 15, 187, 105, 97, 24, 20, 13, 31, 70, 101, 10, 12, 21, 23, 98, 104, 188, 14, 30, 71, 100, 11, 22, 99, 103, 189, 285, 7, 195, 198, 276, 16, 186, 106, 96, 25, 177, 115, 87, 34, 168, 124, 78, 43, 159, 133, 69, 52, 200, 32, 89, 113, 179, 295, 240, 376, 411, 457, 330, 286, 269, 367, 420, 448, 501
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Jun 24 2019

Keywords

Examples

			The sequence starts with 1,2,3,4,5,6,196,197,... and we see indeed that:
the digits of {a(1); a(2)} have sum 1 + 2 = 3 (palindrome) and a(1) + a(2) is a palindrome too (3);
the digits of {a(2); a(3)} have sum 2 + 3 = 5 (palindrome) and a(2) + a(3) is a palindrome too (5);
the digits of {a(3); a(4)} have sum 3 + 4 = 7 (palindrome) and a(3) + a(4) is a palindrome too (7);
the digits of {a(4); a(5)} have sum 4 + 5 = 9 (palindrome) and a(4) + a(5) is a palindrome too (9);
the digits of {a(5); a(6)} have sum 5 + 6 = 11 (palindrome) and a(5) + a(6) is a palindrome too (11);
the digits of {a(6); a(7)} have sum 6 + 1 + 9 + 6 = 22 (palindrome) and a(6) + a(7) = 6 + 196 is a palindrome too (202);
the digits of {a(7); a(8)} have sum 1 + 0 + 7 = 8 (palindrome) and a(7) + a(8) =  is a palindrome too (3);
the digits of {a(8); a(9)} have sum 1 + 9 + 6 + 1 + 9 + 7 = 33 (palindrome) and a(8) + a(9) = 196 + 197 is a palindrome too (393);
etc.

Links

Crossrefs

Cf. A326316 (replace the word "palindrome" by "prime"), A326317 (replace the word "palindrome" by "square"); in A308719 only the sum of the digits is a palindrome.
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.