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A217555
Terms as well as digits are of alternating parity; this is the lexicographically earliest injective sequence with this property.
10
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
1,2
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
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 A342952
KEYWORD
nonn,base
AUTHOR
Eric Angelini and M. F. Hasler, Oct 06 2012
STATUS
approved