

A067076


Numbers n such that 2n + 3 is a prime.


54



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
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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 2n1 is prime; A067076, 2n+3 is a prime.  Jeremy Gardiner, Sep 10 2004
n is in the sequence iff none of the numbers (n3k)/(2k+1), 1<=k<=(n1)/5, is positive integer. [Vladimir Shevelev, May 31 2009]
Zeta(s) = sum[n=1;inf] 1/n^s = 1/12^(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
Mutsumi Suzuki, Vincenzo Librandi's method for sequential primes (Librandi's description in Italian).


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)+n1 = A005097(n)1 = A102781(n+1)1. [R. J. Mathar, Jul 07 2009]
a(n) = A179893(n)  A000040(n). [Odimar Fabeny, Aug 24 2010]


MATHEMATICA

lst={}; Do[If[PrimeQ[2*n+3], AppendTo[lst, n]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)
Select[Range[0, 200], PrimeQ[2#+3]&] (* Harvey P. Dale, Jun 10 2014 *)


PROG

(PARI) { n=0; for (m=0, 10^10, if (isprime(2*m + 3), write("b067076.txt", n++, " ", m); if (n==1000, return)) ) } \\ 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 2nk 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 A245029 A027902 * 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



