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A067076
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Numbers n such that 2n+3 is a prime.
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40
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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; internal format)
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OFFSET
| 1,3
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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 (jeremy.gardiner(AT)btinternet.com), 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 (shevelev(AT)bgu.ac.il), 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 (moongerms(AT)wanadoo.fr), Dec 15 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| a(n) = A006254(n+1)-2 = A086801(n)/2.
a(n) = A089253(n)-4 - Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Dec 14 2003
Conjecture: a(n)=A008507(n)+n-1 = A005097(n)-1 = A102781(n+1)-1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 07 2009]
A179893(n) - A000040(n) [From Odimar Fabeny (aifab(AT)yahoo.com.br), Aug 24 2010]
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MATHEMATICA
| lst={}; Do[If[PrimeQ[2*n+3], AppendTo[lst, n]], {n, 10^3}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 08 2008]
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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 (hjsmithh(AT)sbcglobal.net), May 05 2010]
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CROSSREFS
| Cf. A006254, A086801, A089253.
a(n) = A089192(n)- 5
Sequence in context: A192817 A190853 A027902 * A060686 A004214 A072013
Adjacent sequences: A067073 A067074 A067075 * A067077 A067078 A067079
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KEYWORD
| easy,nonn
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AUTHOR
| David G. Williams (davwill24(AT)aol.com), Aug 17 2002
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