A338841 No odd digit is present in a(n) * a(n+1).

0, 1, 2, 3, 8, 5, 4, 6, 7, 12, 17, 24, 10, 20, 11, 22, 13, 16, 14, 19, 32, 9, 52, 39, 58, 36, 18, 26, 31, 28, 15, 40, 21, 42, 53, 54, 46, 44, 47, 60, 34, 59, 38, 69, 94, 30, 68, 33, 62, 43, 48, 50, 56, 73, 88, 23, 96, 25, 80, 35, 64, 41, 104, 27, 84, 51, 122, 71, 66, 37, 72, 29, 76, 79, 112, 74, 63, 102, 61

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

• nonn
• base
• look

Comments

This is the lexicographically earliest sequence of distinct nonnegative terms with this property and also a permutation of the nonnegative integers.

Examples

			a(1) * a(2) = 0 * 1 = 0 (no odd digit is present);
a(2) * a(3) = 1 * 2 = 2 (no odd digit is present);
a(3) * a(4) = 2 * 3 = 6 (no odd digit is present);
a(4) * a(5) = 3 * 8 = 24 (no odd digit is present); etc.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5000
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A014263 (no odd digits).

Cf. A338839, A338840, A338842, A338843, A338844, A338845, A338846 (variants on the same idea).

Programs

Mathematica

Block[{a = {0}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], OddQ]], k++]; AppendTo[a, k]], {i, 2, 79}]; a] (* Michael De Vlieger, Nov 12 2020 *)