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A217555 Terms as well as digits are of alternating parity; this is the lexicographically earliest injective sequence with this property. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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)

PROG

(PARI) {a(n, show=1, a=1, u)=for( i=2, n, u+=1<<a; show & print1(a", "); for(t=1, 9e9, bittest(u, t) & next; bittest(t+a, 0) || next; !bittest(a%10 + t\10^(#Str(t)-1), 0) & (t+=10^(#Str(t)-1)-1) & next; my(tt=t); while( tt>9, bittest( tt+0+tt\=10, 0 ) || next(2)); a=t; break )); a}

CROSSREFS

Sequence A217556 is a simplified variant.

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

Sequence in context: A002998 A061276 A249515 * A137667 A117954 A029966

Adjacent sequences:  A217552 A217553 A217554 * A217556 A217557 A217558

KEYWORD

nonn,base

AUTHOR

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

STATUS

approved

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Last modified March 6 00:22 EST 2021. Contains 341835 sequences. (Running on oeis4.)