

A211204


a(1) = 2; for n > 1, a(n) > a(n1) is the smallest prime for which the set {a(1), a(2), ..., a(n)} lacks at least one residue modulo every odd prime less than or equal to a(n).


2



2, 3, 5, 11, 17, 23, 41, 47, 53, 71, 83, 101, 107, 113, 131, 137, 167, 173, 191, 197, 233, 251, 257, 263, 311, 317, 347, 353, 401, 431, 443, 461, 467, 503, 521, 563, 593, 641, 647, 653, 677, 683, 701, 743, 761, 773, 797, 827, 857, 863, 881, 911, 941, 947, 971
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OFFSET

1,1


COMMENTS

By construction, for every odd prime p > 1, the sequence does not contain a full residue system modulo p. For n >= 4, all differences a(n)  a(n1) are multiples of 6; otherwise said, a(n) == 5 (mod 6).
Conjecture: The sequence contains infinitely many "twins" with a(n)a(n1) = 6.
All terms greater than 3 are 2 mod 3, so the sequence does not contain a complete residue system mod 3; all terms are not 4 mod 5, so the sequence does not contain a complete residue system mod 5; since 7 is absent in the sequence, there is not a complete residue system mod 7.


LINKS

Vladimir Shevelev and Peter J. C. Moses, Table of n, a(n) for n = 1..92


CROSSREFS

Cf. A210537.
Sequence in context: A049595 A258039 A107438 * A023206 A049565 A094480
Adjacent sequences: A211201 A211202 A211203 * A211205 A211206 A211207


KEYWORD

nonn


AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Feb 04 2013


EXTENSIONS

Edited by M. F. Hasler, Feb 13 2013


STATUS

approved



