login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053001 Largest prime < n^2. 23
3, 7, 13, 23, 31, 47, 61, 79, 97, 113, 139, 167, 193, 223, 251, 283, 317, 359, 397, 439, 479, 523, 571, 619, 673, 727, 773, 839, 887, 953, 1021, 1087, 1153, 1223, 1291, 1367, 1439, 1511, 1597, 1669, 1759, 1847, 1933, 2017, 2113, 2207, 2297, 2399, 2477, 2593 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Suggested by Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2.

Legendre's conjecture is equivalent to a(n) > (n-1)^2. - John W. Nicholson, Dec 11 2013

REFERENCES

Octavian Cira, Smarandache's Conjecture on Consecutive Primes, International J.Math. Combin. Vol. 4 (2014), 69-91; http://mathcombin.com/upload/file/20150127/1422320940239094100.pdf#page=74

J. R. Goldman, The Queen of Mathematics, 1998, p. 82.

LINKS

T. D. Noe, Table of n, a(n) for n=2..1000

FORMULA

a(n) = A007917(A000290(n)). - Reinhard Zumkeller, Jun 07 2015

MAPLE

[seq(prevprime(i^2), i=2..100)];

MATHEMATICA

Table[Prime[PrimePi[n^2]], {n, 2, 60}] (* Stefan Steinerberger, Apr 01 2006 *)

Table[NextPrime[n^2, -1], {n, 2, 60}] (* Jean-Fran├žois Alcover, Oct 14 2013 *)

PROG

(PARI) a(n) = precprime(n^2) \\ Michel Marcus, Oct 14 2013

(Haskell)

a053001 = a007917 . a000290  -- Reinhard Zumkeller, Jun 07 2015

CROSSREFS

Cf. A007491, A053000, A014085.

Cf. A007917, A000290.

Sequence in context: A081662 A091652 A134197 * A053607 A209407 A124129

Adjacent sequences:  A052998 A052999 A053000 * A053002 A053003 A053004

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Feb 21 2000

EXTENSIONS

More terms from James A. Sellers, Feb 22 2000

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified March 29 08:58 EDT 2017. Contains 284268 sequences.