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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 04:02 EDT 2019. Contains 328106 sequences. (Running on oeis4.)