A180724 a(n) = n^2 + largest prime < n^2.

7, 16, 29, 48, 67, 96, 125, 160, 197, 234, 283, 336, 389, 448, 507, 572, 641, 720, 797, 880, 963, 1052, 1147, 1244, 1349, 1456, 1557, 1680, 1787, 1914, 2045, 2176, 2309, 2448, 2587, 2736, 2883, 3032, 3197, 3350, 3523, 3696, 3869, 4042, 4229, 4416, 4601

Offset

2,1

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Formula

4 + 3 = 7; 9 + 7 = 16; 16 + 13 = 29; 25 + 23 = 48;

a(n) = n^2+A053001(n). - R. J. Mathar, Sep 19 2010

2n^2 - O(n^1.05) < a(n) < 2n^2. (Probably a much tighter lower bound is true.) - Charles R Greathouse IV, Jan 31 2023

Mathematica

#+NextPrime[#, -1]&/@(Range[2, 50]^2) (* Harvey P. Dale, Apr 08 2023 *)

Prog

(PARI) a(n) = n^2 + precprime(n^2-1); \\ Michel Marcus, Aug 23 2013

Crossrefs

Sequence in context: A133694 A024627 A211784 * A212866 A234717 A364352

Adjacent sequences: A180721 A180722 A180723 * A180725 A180726 A180727

Keyword

nonn,easy

Author

Ian Stewart, Sep 18 2010

Status

approved