A217556 -id:A217556 - cp's OEIS frontend

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

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

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

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

Sequence A217556 is a simplified variant.

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

{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}

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)

A217559 Terms as well as ending/starting digits have alternating primality; this is the lexicographically earliest injective sequence with this property.

Original entry on oeis.org

1, 2, 4, 3, 6, 5, 8, 7, 9, 23, 10, 29, 22, 11, 24, 31, 25, 13, 12, 17, 14, 37, 15, 19, 26, 53, 16, 59, 28, 71, 30, 73, 18, 79, 20, 211, 21, 223, 48, 227, 49, 229, 27, 41, 32, 43, 44, 233, 45, 47, 46, 239, 33, 61, 34, 241, 35, 67, 60, 251, 36, 257, 62, 83, 63, 89, 38, 263, 64, 269, 39, 271, 50, 277

Offset: 1

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

Exactly every other term is prime; moreover the ending digit of a(n) and the initial digit of a(n+1) are never both prime or both composite.

E. Angelini, Non-primes/primes: integers and digits alternate, SeqFan mailing list, Oct 06 2012

This is a simplified variant of A217560.

See also A217555, A217556, where "primality" is replaced by "parity".

A217559(n,show_all=0,a=1,u)={for( i=2, n, u+=1<

A217560 Terms as well as digits have alternating primality; this is the lexicographically earliest injective sequence with this property.

Original entry on oeis.org

1, 2, 4, 3, 6, 5, 8, 7, 9, 29, 20, 31, 21, 59, 24, 71, 26, 79, 28, 263, 12, 13, 15, 17, 42, 43, 45, 47, 62, 67, 63, 83, 65, 97, 82, 131, 30, 283, 85, 139, 34, 293, 87, 151, 36, 307, 92, 179, 38, 313, 93, 421, 39, 317, 95, 431, 50, 347, 120, 367, 121, 383, 124, 397, 126, 503, 128, 547, 129, 563, 130, 587, 134, 593, 136, 743, 138, 787

Offset: 1

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

Exactly every other term, and also every other digit (in concatenated terms) is prime.

Carole Dubois, Table of n, a(n) for n = 1..5292
E. Angelini, Non-primes/primes: integers and digits alternate, SeqFan mailing list, Oct 06 2012
Carole Dubois, Graph with even ranges and odd ranges separated

The sequence A217559 is a simplified variant.

See also A217555, A217556, where "primality" is replaced by "parity".

Values from a(26)=43 on corrected by Jean-Marc Falcoz, Oct 10 2012

cp's OEIS Frontend

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

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A217559 Terms as well as ending/starting digits have alternating primality; this is the lexicographically earliest injective sequence with this property.

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Crossrefs

Programs

PARI

A217560 Terms as well as digits have alternating primality; this is the lexicographically earliest injective sequence with this property.

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