login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A066872 p^2 + 1 as p runs through the primes. 11
5, 10, 26, 50, 122, 170, 290, 362, 530, 842, 962, 1370, 1682, 1850, 2210, 2810, 3482, 3722, 4490, 5042, 5330, 6242, 6890, 7922, 9410, 10202, 10610, 11450, 11882, 12770, 16130, 17162, 18770, 19322, 22202, 22802, 24650, 26570, 27890, 29930, 32042 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From R. J. Mathar, Aug 28 2011: (Start)

There are at least three "natural" embeddings of this function into multiplicative functions b(n), c(n) and d(n):

(i) The first is b(n) = 1, 5, 10, 0, 26, 0, 50, ... (n>=1) with b(p) = p^2+1, b(p^e)=0 if e>=2, substituting zero for all composite n.

(ii) The second is c(n) = 1, 5, 10, 9, 26, 50, 50, 17, 28, 130, ... (n>=1) with c(p^e)= p^(e+1)+1.

(iii) The third is d(n) = 1, 5, 10, 5, 26, 50, 50, 5, 10, 130, ... (n>=1) with d(p^e) = p^2+1 if e>=1. (End)

For n > 1, a(n)/2 is of the form 4*k+1. - Altug Alkan, Apr 08 2016

LINKS

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

R. P. Boas & N. J. A. Sloane, Correspondence, 1974

FORMULA

a(n) = A002522(A000040(n)). - Altug Alkan, Apr 08 2016

a(n) = A000010(A000040(n)^2) + A323599(A000040(n)^2). - Torlach Rush, Jan 25 2019

MATHEMATICA

Table[Prime[n]^2 + 1, {n, 41}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)

PROG

(PARI) { for (n=1, 1000, write("b066872.txt", n, " ", prime(n)^2 + 1) ) } \\ Harry J. Smith, Apr 02 2010

(MAGMA) [p^2+1: p in PrimesUpTo(300)]; // Vincenzo Librandi, Oct 31 2014

CROSSREFS

Cf. A002522, A000010, A000040, A323599.

Sequence in context: A324005 A166388 A290055 * A301537 A063478 A128665

Adjacent sequences:  A066869 A066870 A066871 * A066873 A066874 A066875

KEYWORD

easy,nonn

AUTHOR

Joseph L. Pe, Jan 21 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 21 22:47 EST 2020. Contains 331129 sequences. (Running on oeis4.)