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

Author

Charles R Greathouse IV, Feb 05 2011

Keywords

• nonn
• easy

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

Crossrefs

Cf. A141468.

Complement of A018252. - Arkadiusz Wesolowski, Sep 15 2011

Programs

Mathematica

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

PARI

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