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

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

1,2

Comments

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

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Example

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.

Crossrefs

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

Sequence in context: A338833 A342786 A293474 * A268217 A254793 A353715

Adjacent sequences: A308724 A308725 A308726 * A308728 A308729 A308730

Keyword

base,nonn

Author

Jean-Marc Falcoz and Eric Angelini, Jun 20 2019

Status

approved