

A210537


a(1)=3; for n>1, a(n)>a(n1) is the minimal for which the set {a(1),a(2),...,a(n)} lacks at least one residue mod 2, 3, ....


3



3, 5, 9, 11, 15, 21, 23, 29, 33, 35, 39, 45, 51, 53, 59, 65, 71, 75, 81, 89, 93, 99, 101, 105, 113, 119, 123, 131, 135, 141, 143, 149, 155, 159, 161, 165, 171, 179, 185, 189, 191, 201, 203, 213, 215, 219, 233, 243, 245, 249, 255, 263, 269, 273, 275, 281, 285, 291, 309, 311, 315, 323, 339, 341, 345, 351, 353, 365, 375, 383, 389, 395, 399, 413, 423, 425, 429, 431, 441, 453, 455, 465, 471, 473, 479, 491, 495, 501
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OFFSET

1,1


COMMENTS

By the construction, for every N>1, the sequence does not contain a full residue system modulo N. The difference of any two primes greater than 3 in this sequence is a multiple of 6.
Conjectures: (1) the sequence contains infinitely many "twins" when such differences equal 6; (2) lim a(n)/prime(n)=1 as n goes to infinity.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Charles R Greathouse IV, PARI/GP code for computing terms of this sequence


EXAMPLE

All terms are odd, so {a(1), ...,} does not contain a complete residue system mod 2. All terms are 0 or 2 mod 3, so the sequence does not contain a complete residue system mod 3.


MATHEMATICA

s = {3}; Do[AppendTo[s, 2+Last@s]; While[r = 1+Range@Length@s; Max[Length /@ Union /@ (Mod[s, #]& /@ r)  r] == 0, s[[1]]++], {87}]; s (* Giovanni Resta, Jan 29 2013 *)


PROG

(PARI) See Greathouse link.


CROSSREFS

Sequence in context: A151922 A233762 A104635 * A199407 A261141 A283594
Adjacent sequences: A210534 A210535 A210536 * A210538 A210539 A210540


KEYWORD

nonn


AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Jan 29 2013


STATUS

approved



