A338840 No even digit is present in a(n) + a(n+1).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 12, 19, 14, 17, 16, 15, 18, 13, 20, 11, 22, 29, 24, 27, 26, 25, 28, 23, 30, 41, 32, 39, 34, 37, 36, 35, 38, 33, 40, 31, 42, 49, 44, 47, 46, 45, 48, 43, 50, 61, 52, 59, 54, 57, 56, 55, 58, 53, 60, 51, 62, 69, 64, 67, 66, 65, 68, 63, 70, 81, 72, 79, 74, 77, 76, 75, 78, 73

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

• base
• nonn

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 = 1 (no even digit is present);
a(2) + a(3) = 1 + 2 = 3 (no even digit is present);
a(3) + a(4) = 2 + 3 = 5 (no even digit is present);
...
a(6) + a(7) = 5 + 6 = 11 (no even digit is present); etc.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5001
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A014261 (no even digits).

Cf. A338839, A338841, 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], EvenQ]], k++]; AppendTo[a, k]], {i, 2, 80}]; a] (* Michael De Vlieger, Nov 12 2020 *)