A061725 p^2 + 2 where p is a prime.

6, 11, 27, 51, 123, 171, 291, 363, 531, 843, 963, 1371, 1683, 1851, 2211, 2811, 3483, 3723, 4491, 5043, 5331, 6243, 6891, 7923, 9411, 10203, 10611, 11451, 11883, 12771, 16131, 17163, 18771, 19323, 22203, 22803, 24651, 26571, 27891, 29931

Offset: 1

Author

Jason Earls, Jun 23 2001

Keywords

• easy
• nonn

Comments

For any n >= 3, a(n) is of the form a(n) = 27 + 6m, m >= 0 integer. This follows from the simple fact that for any prime p >= 5, (p + 5)(p - 5) is divisible by 6. - Shai Covo (green355(AT)netvision.net.il), Oct 04 2010

References

• David M. Burton, Elementary Number Theory, Allyn and Bacon, Inc. Boston, MA, 1976, pp. 51.
• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Example 5.1 on page 153.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001248.

Programs

Magma

[p^2+2: p in PrimesUpTo(200)]; // Vincenzo Librandi, Mar 22 2015

Maple

A061725:=n->ithprime(n)^2+2: seq(A061725(n), n=1..50); # Wesley Ivan Hurt, Mar 17 2015

Mathematica

Prime[Range[40]]^2 + 2 (* Geoffrey Critzer, Feb 01 2015 *)

PARI

v=[]; for(n=1,100,v=concat(v,(prime(n)^2)+2)); v

PARI

{ n=0; forprime (p=2, prime(1000), write("b061725.txt", n++, " ", p^2 + 2) ) } \\ Harry J. Smith, Jul 27 2009