A182986 Zero together with the prime numbers (A000040).

0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset

1,2

Comments

These numbers are the possible characteristics of a field.

First differences are in A054541. - Omar E. Pol, Oct 31 2013

Also A158611 without its second term. - Omar E. Pol, Nov 01 2013

The ideals generated by a(n) form Spec(Z), the set of prime ideals of the ring of integers. Due to its importance in algebraic geometry, algebraic geometers often consider 0 to be an honorary prime. - Keith J. Bauer, Jan 09 2024

Links

Table of n, a(n) for n=1..58.

Mathematica

Prepend[Table[Prime[n], {n, 60}], 0] (* Arkadiusz Wesolowski, Sep 15 2011 *)
NestList[ NextPrime, 0, 57] (* Robert G. Wilson v, Jul 21 2015 *)

Prog

(PARI) a(n)=if(n>1, prime(n-1), 0) \\ Charles R Greathouse IV, Jul 15 2013

Crossrefs

Cf. A141468.

Complement of A018252. - Arkadiusz Wesolowski, Sep 15 2011

Sequence in context: A295425 A158611 A226159 * A000040 A008578 A216883

Adjacent sequences: A182983 A182984 A182985 * A182987 A182988 A182989

Keyword

nonn,easy

Author

Charles R Greathouse IV, Feb 05 2011

Status

approved