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A217555
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Terms as well as digits are of alternating parity; this is the lexicographically earliest injective sequence with this property.
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5
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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
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FORMULA
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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)
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PROG
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(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}
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CROSSREFS
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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
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KEYWORD
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nonn,base
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AUTHOR
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Eric Angelini and M. F. Hasler, Oct 06 2012
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STATUS
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approved
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