A217555 Terms as well as digits are of alternating parity; this is the lexicographically earliest injective sequence with this property.

1, 2, 3, 4, 5, 6, 7, 8, 9, 210, 101, 212, 103, 214, 105, 216, 107, 218, 109, 230, 121, 232, 123, 234, 125, 236, 127, 238, 129, 250, 141, 252, 143, 254, 145, 256, 147, 258, 149, 270, 161, 272, 163, 274, 165, 276, 167, 278, 169, 290, 181, 292, 183

Offset: 1

Author

Eric Angelini and M. F. Hasler, Oct 06 2012

Keywords

• nonn
• base

Comments

The sum of two successive terms is odd and the sum of two successive digits is odd, too. The sequence could be started with an additional 0 and then be extended always with the smallest integer not yet present in the sequence and not leading to a contradiction. - Eric Angelini and Jean-Marc Falcoz, Jan 31 2017

Links

• Carole Dubois, Table of n, a(n) for n = 1..15484
• Eric Angelini, Odd/even: integers and digits alternate, SeqFan mailing list, Oct 06 2012

Crossrefs

Sequence A217556 is a simplified variant.

See also A217559, A217560, where "parity" is replaced by "primality".

Programs

PARI

{a(n,show=1,a=1,u)=for( i=2, n, u+=1<9, bittest( tt+0+tt\=10, 0 ) || next(2)); a=t; break )); a}

Formula

Conjectures from Colin Barker, Jan 16 2020: (Start)

G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + 201*x^9 - 110*x^10 + 110*x^11 - 110*x^12 + 110*x^13 - 110*x^14 + 110*x^15 - 110*x^16 + 110*x^17 - 110*x^18 - 80*x^19) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-1) + a(n-10) - a(n-11) for n>20.

(End)