login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A073497 a(n) = n^2 - prime(n). 3
-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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

Sequence in context: A099980 A281314 A004630 * A244941 A086192 A105503

Adjacent sequences:  A073494 A073495 A073496 * A073498 A073499 A073500

KEYWORD

sign,easy

AUTHOR

Werner D. Sand, Aug 27 2002

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 3 10:25 EDT 2022. Contains 355050 sequences. (Running on oeis4.)