A210537 a(1)=3; for n>1, a(n)>a(n-1) is the minimal for which the set {a(1),a(2),...,a(n)} lacks at least one residue mod 2, 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

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