A066883 -id:A066883 - cp's OEIS frontend

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

Enoch Haga, Jan 22 2002

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

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.

Cf. A066883, A066886.
Cf. A088165, A140480.
Cf. A084921.
Partial sums of A124434.

[(NthPrime(n)^2+1)/2 : n in [2..50]]; // Wesley Ivan Hurt, Jun 23 2015

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

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

A066885(n) = (prime(n)^2+1)/2 \\ Michael B. Porter, Dec 14 2009

{ for (n=2, 1000, write("b066885.txt", n, " ", (prime(n)^2 + 1)/2) ) } \\ Harry J. Smith, Apr 04 2010

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

Edited by Dean Hickerson, Jun 08 2002

A066886 Sum of the elements in any transversal of a prime(n) X prime(n) array containing the numbers from 1 to prime(n)^2 in standard order.

Original entry on oeis.org

5, 15, 65, 175, 671, 1105, 2465, 3439, 6095, 12209, 14911, 25345, 34481, 39775, 51935, 74465, 102719, 113521, 150415, 178991, 194545, 246559, 285935, 352529, 456385, 515201, 546415, 612575, 647569, 721505, 1024255, 1124111, 1285745

Offset: 1

Enoch Haga, Jan 22 2002

a(n) is the sum of the primes in a prime(n) X prime(n) example of Haga's conjecture (see link below).

Robert Israel, Table of n, a(n) for n = 1..10000
Carlos Rivera, The prime puzzles & problems connection, conjecture 26, The Prime Puzzles and Problems Connection.

Cf. A005097, A006003, A006254, A066883, A066885.

map(t -> t*(t^2+1)/2, [seq(ithprime(i),i=1..100)]); # Robert Israel, Apr 04 2018

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

apply(x->(x*(x^2+1)/2), primes(100)) \\ Michel Marcus, Apr 04 2018

a(n) = prime(n)*(prime(n)^2+1)/2, where prime(n) is the n-th prime.
a(n) = A006003(prime(n)). - Michel Marcus, Apr 04 2018
a(n) = A006254(n-1)^4 - A005097(n-1)^4, for n>1. - Dimitris Valianatos, Apr 10 2018

Edited by Dean Hickerson, Jun 08 2002

cp's OEIS Frontend

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

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A066886 Sum of the elements in any transversal of a prime(n) X prime(n) array containing the numbers from 1 to prime(n)^2 in standard order.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions