

A053000


(Smallest prime > n^2)  n^2.


19



2, 1, 1, 2, 1, 4, 1, 4, 3, 2, 1, 6, 5, 4, 1, 2, 1, 4, 7, 6, 1, 2, 3, 12, 1, 6, 1, 4, 3, 12, 7, 6, 7, 2, 7, 4, 1, 4, 3, 2, 1, 12, 13, 12, 13, 2, 13, 4, 5, 10, 3, 8, 3, 10, 1, 12, 1, 2, 7, 10, 7, 6, 3, 20, 3, 4, 1, 4, 13, 22, 3, 10, 5, 4, 1, 14, 3, 10, 5, 6, 21, 2, 9, 10, 1, 4, 15, 4, 9, 6, 1, 6, 3, 14
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OFFSET

0,1


COMMENTS

Suggested by Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2.
Record values are listed in A070317, their indices in A070316.  M. F. Hasler, Mar 23 2013


REFERENCES

J. R. Goldman, The Queen of Mathematics, 1998, p. 82.


LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000


FORMULA

a(n) = A013632(n^2).  Robert Israel, Jul 06 2015


MAPLE

A053000 := n>nextprime(n^2)n^2;


MATHEMATICA

nxt[n_]:=Module[{n2=n^2}, NextPrime[n2]n2]
nxt/@Range[0, 100] (* Harvey P. Dale, Dec 20 2010 *)


PROG

(PARI) A053000(n)=nextprime(n^2)n^2 \\ M. F. Hasler, Mar 23 2013
(MAGMA) [NextPrime(n^2)  n^2: n in [0..100]]; // Vincenzo Librandi, Jul 06 2015


CROSSREFS

Cf. A007491, A013632, A053001, A014085, A070316, A085099, A058055, A069003.
Sequence in context: A276376 A165585 A082506 * A002070 A326376 A106052
Adjacent sequences: A052997 A052998 A052999 * A053001 A053002 A053003


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane, Feb 21 2000


EXTENSIONS

More terms from James A. Sellers, Feb 22 2000


STATUS

approved



