A073497 a(n) = n^2 - prime(n).

-1, 1, 4, 9, 14, 23, 32, 45, 58, 71, 90, 107, 128, 153, 178, 203, 230, 263, 294, 329, 368, 405, 446, 487, 528, 575, 626, 677, 732, 787, 834, 893, 952, 1017, 1076, 1145, 1212, 1281, 1354, 1427, 1502, 1583, 1658, 1743, 1828, 1917, 1998, 2081, 2174, 2271, 2368

Offset: 1

Author

Werner D. Sand, Aug 27 2002

Keywords

• sign
• easy

Comments

a(n) is never a perfect square for n>=5. [Proof: assume on the contrary n^2 - prime(n) = k^2, equivalent to (n+k)*(n-k) = prime(n). Since prime(n) cannot be the product of two nontrivial factors, this equation can only hold for k=n-1, i.e., prime(n)=2n-1. This contradicts the assumption and completes the proof.] - Alexander R. Povolotsky, Oct 01 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Programs

Magma

[n^2 - NthPrime(n): n in [1..100] ]; // Vincenzo Librandi, Apr 12 2011

Mathematica

Table[n^2 - Prime[n], {n, 1, 55}]

PARI

for(n=1,51,print1(n*n-prime(n),","))

Extensions

More terms from Klaus Brockhaus and Robert G. Wilson v, Aug 28 2002