A066885 a(n) = (prime(n)^2 + 1)/2.

5, 13, 25, 61, 85, 145, 181, 265, 421, 481, 685, 841, 925, 1105, 1405, 1741, 1861, 2245, 2521, 2665, 3121, 3445, 3961, 4705, 5101, 5305, 5725, 5941, 6385, 8065, 8581, 9385, 9661, 11101, 11401, 12325, 13285, 13945, 14965, 16021, 16381, 18241, 18625

Offset

2,1

Comments

a(n) is the average of the numbers from 1 to prime(n)^2. It's also the average of the primes in a prime(n) X prime(n) example of Haga's conjecture (see link below).

If a(n) is a square c^2, then prime(n) is an NSW prime (A088165) and a prime RMS number (A140480). - Ctibor O. Zizka, Aug 26 2008

The sequence starts with a(2) = (3^2 + 1)/2 = 5 since a(1) would be (2^2 + 1)/2 = 5/2. - Michael B. Porter, Dec 14 2009

Links

Harry J. Smith, Table of n, a(n) for n = 2..1000

Carlos Rivera, Conjecture 26. The Calendar-like square Conjecture, The Prime Puzzles and Problems Connection.

Formula

a(n) = 1 + A084921(n). - R. J. Mathar, Sep 30 2011

a(n) mod 4 = 1. - Altug Alkan, Apr 08 2016

Product_{n>=2} (1 - 1/a(n)) = 2/3. - Amiram Eldar, Jun 03 2022

Maple

A066885:=n->(ithprime(n)^2+1)/2: seq(A066885(n), n=2..50); # Wesley Ivan Hurt, Jun 23 2015

Mathematica

a[n_] := (Prime[n]^2+1)/2; Table[a[n], {n, 2, 50}]

Prog

(PARI) A066885(n) = (prime(n)^2+1)/2 \\ Michael B. Porter, Dec 14 2009
(PARI) { for (n=2, 1000, write("b066885.txt", n, " ", (prime(n)^2 + 1)/2) ) } \\ Harry J. Smith, Apr 04 2010
(Magma) [(NthPrime(n)^2+1)/2 : n in [2..50]]; // Wesley Ivan Hurt, Jun 23 2015

Crossrefs

Cf. A066883, A066886.

Cf. A088165, A140480.

Cf. A084921.

Partial sums of A124434.

Sequence in context: A146140 A146283 A026373 * A147151 A057288 A107466

Adjacent sequences: A066882 A066883 A066884 * A066886 A066887 A066888

Keyword

easy,nonn

Author

Enoch Haga, Jan 22 2002

Extensions

Edited by Dean Hickerson, Jun 08 2002

Status

approved