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

 

Logo

Many excellent designs for a new banner were submitted. We will use the best of them in rotation.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A067076 Numbers n such that 2n + 3 is a prime. 53
0, 1, 2, 4, 5, 7, 8, 10, 13, 14, 17, 19, 20, 22, 25, 28, 29, 32, 34, 35, 38, 40, 43, 47, 49, 50, 52, 53, 55, 62, 64, 67, 68, 73, 74, 77, 80, 82, 85, 88, 89, 94, 95, 97, 98, 104, 110, 112, 113, 115, 118, 119, 124, 127, 130, 133, 134, 137, 139, 140, 145, 152, 154, 155 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The following sequences (allowing offset of first term) all appear to have the same parity: A034953, triangular numbers with prime indices; A054269, length of period of continued fraction for sqrt(p), p prime; A082749, difference between the sum of next prime(n) natural numbers and the sum of next n primes; A006254, numbers n such that 2n-1 is prime; A067076, 2n+3 is a prime. - Jeremy Gardiner, Sep 10 2004

n is in the sequence iff none of the numbers (n-3k)/(2k+1), 1<=k<=(n-1)/5, is positive integer. [From Vladimir Shevelev, May 31 2009]

Zeta(s) = sum[n=1;inf] 1/n^s = 1/1-2^(-s) * prod[p=prime=(2*A067076)+3] 1/(1 - (2*A067076+3)^(-s)) [From Eric Desbiaux, Dec 15 2009]

This sequence is a subsequence of A047949. - Jason Kimberley, Aug 30 2012

Solutions of the equation (2*n+3)' = 1, where n' is the arithmetic derivative of n. [Paolo P. Lava, Nov 15 2012].

LINKS

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

FORMULA

a(n) = A006254(n+1)-2 = A086801(n)/2.

a(n) = A089253(n)-4 - Giovanni Teofilatto, Dec 14 2003

Conjecture: a(n)=A008507(n)+n-1 = A005097(n)-1 = A102781(n+1)-1. [From R. J. Mathar, Jul 07 2009]

A179893(n) - A000040(n) [From Odimar Fabeny, Aug 24 2010]

MATHEMATICA

lst={}; Do[If[PrimeQ[2*n+3], AppendTo[lst, n]], {n, 10^3}]; lst [From Vladimir Joseph Stephan Orlovsky, Sep 08 2008]

PROG

(PARI) { n=0; for (m=0, 10^10, if (isprime(2*m + 3), write("b067076.txt", n++, " ", m); if (n==1000, return)) ) } [From Harry J. Smith, May 05 2010]

(MAGMA)[n: n in [0..200]| IsPrime(2*n+3)]; // Vincenzo Librandi, Feb 23 2012

CROSSREFS

Cf. A086801, A047949.

Numbers n such that 2n+k is prime: A005097 (k=1), this seq(k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19). - Jason Kimberley, Sep 07 2012

Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

Sequence in context: A190853 A027902 A225783 * A060686 A004214 A231979

Adjacent sequences:  A067073 A067074 A067075 * A067077 A067078 A067079

KEYWORD

easy,nonn

AUTHOR

David G. Williams (davwill24(AT)aol.com), Aug 17 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified April 16 00:40 EDT 2014. Contains 240534 sequences.