A020498 a(n) is the least number > a(n-1) such that a(1) through a(n) do not contain all residues modulo any prime.

1, 3, 7, 9, 13, 19, 21, 27, 31, 33, 37, 43, 49, 51, 57, 63, 69, 73, 79, 87, 91, 97, 99, 103, 111, 117, 121, 129, 133, 139, 141, 147, 153, 157, 159, 163, 169, 177, 183, 187, 189, 199, 201, 211, 213, 217, 231, 241, 243, 247, 253, 261, 267, 271, 273, 279, 283, 289

Offset

1,2

Comments

Conjecturally, a(n) is the smallest number such that n primes occur infinitely often among (x+a(1), ...,x+a(n)).

References

R. K. Guy's "Unsolved Problems in Number Theory" (2nd edition, Springer, 1994), Section A9.

Links

David W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020497, A008407.

Sequence in context: A141544 A172407 A088649 * A200567 A107771 A364614

Adjacent sequences: A020495 A020496 A020497 * A020499 A020500 A020501

Keyword

nonn

Author

Robert G. Wilson v and Christopher E. Thompson

Extensions

More terms from David Wasserman, Aug 17 2005

Old name has been interchanged with Wasserman's comment, as old name only a conjectural definition of the sequence. Edited by Christopher J. Smyth, May 12 2016

Status

approved