A342266 Lexicographically earliest sequence of distinct nonnegative terms such that both a(n) and a(n) * a(n+1) have digits in nondecreasing order.

0, 1, 2, 3, 4, 6, 8, 7, 5, 9, 13, 12, 14, 16, 18, 26, 44, 27, 17, 15, 23, 29, 46, 28, 48, 47, 24, 19, 117, 38, 36, 33, 34, 37, 67, 35, 127, 114, 39, 57, 78, 146, 236, 58, 77, 1444, 177, 157, 2477, 144, 247, 45, 25, 49, 227, 147, 257, 1777, 12568, 116, 68, 66, 118, 113, 59, 226, 148, 166, 134, 167, 334

Offset

1,3

Comments

10 is obviously the first integer not present in the sequence as 1 > 0; 11 will never show either because the result of a(n) * 11 is already in the sequence or because the said result has digits in contradiction with the definition.

It would be good to have a proof that there is an infinite sequence with the desired property. It could happen then any choice for any number of initial terms will eventually fail. - David A. Corneth and N. J. A. Sloane, Mar 07 2021

The authors agree, but are unable to give the desired proof. So it is indeed possible that this sequence is wrong from the first term on.

Links

Table of n, a(n) for n=1..71.

Carole Dubois, Table of n, a(n) for n = 1..138 (terms calculated with a(n+1) < a(n)*1000, (backtracking when not found inside this limit)).

Example

a(5) = 4 and a(6) = 6 have product 24: the three numbers have digits in nondecreasing order;
a(6) = 6 and a(7) = 8 have product 48: the three numbers have digits in nondecreasing order;
a(7) = 8 and a(7) = 7 have product 56: the three numbers have digits in nondecreasing order; etc.

Crossrefs

Cf. A009994 (numbers with digits in nondecreasing order), A342264 and A342265 (variations on the same idea).

Sequence in context: A277519 A277623 A082315 * A082320 A285111 A253566

Adjacent sequences: A342263 A342264 A342265 * A342267 A342268 A342269

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Mar 07 2021

Status

approved