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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014342 Convolution of primes with themselves. 8
4, 12, 29, 58, 111, 188, 305, 462, 679, 968, 1337, 1806, 2391, 3104, 3953, 4978, 6175, 7568, 9185, 11030, 13143, 15516, 18177, 21150, 24471, 28152, 32197, 36678, 41543, 46828, 52621, 58874, 65659, 73000, 80949, 89462, 98631, 108396, 118869, 130102 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{i=1..n} p(i) * p(n+1-i), where p(i) is the i-th prime.

G.f.: (b(x)^2)/x, where b(x) is the g.f. of A000040. - Mario C. Enriquez, Dec 13 2016

EXAMPLE

a(2)=12 because a(2) = p(1)*p(2)+p(2)*p(1) = 2*3+3*2 = 12.

MAPLE

A014342:=n->add(ithprime(i)*ithprime(n+1-i), i=1..n): seq(A014342(n), n=1..50); # Wesley Ivan Hurt, Dec 14 2016

MATHEMATICA

Table[Sum[Prime[i] Prime[n + 1 - i], {i, n}], {n, 40}] (* Michael De Vlieger, Dec 13 2016 *)

PROG

(PARI) {m=40; u=vector(m, x, prime(x)); for(n=1, m, v=vecextract(u, concat("1..", n)); w=vector(n, x, u[n+1-x]); print1(v*w~, ", "))} \\ Klaus Brockhaus, Apr 28 2004

(Haskell)

a014342 n = a014342_list !! (n-1)

a014342_list= f (tail a000040_list) [head a000040_list] 1 where

   f (p:ps) qs k = sum (zipWith (*) qs $ reverse qs) :

                   f ps (p : qs) (k + 1)

-- Reinhard Zumkeller, Apr 07 2014, Mar 08 2012

(MAGMA) [&+[NthPrime(n-i+1)*NthPrime(i): i in [1..n]]: n in [1..40]]; // Bruno Berselli, Apr 12 2016

CROSSREFS

Cf. A000040, A023626, A024697, A025129, A209403.

Sequence in context: A091521 A050898 A009845 * A086274 A174121 A128563

Adjacent sequences:  A014339 A014340 A014341 * A014343 A014344 A014345

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Felix Goldberg (felixg(AT)tx.technion.ac.il), Feb 01 2001

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 July 26 00:44 EDT 2017. Contains 289798 sequences.