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

Author

Ian Stewart, Sep 18 2010

Keywords

• nonn
• easy

Links

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

Programs

Mathematica

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

PARI

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

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