

A040040


Average of twin prime pairs (A014574), divided by 2. Equivalently, 2*a(n)1 and 2*a(n)+1 are primes.


41



2, 3, 6, 9, 15, 21, 30, 36, 51, 54, 69, 75, 90, 96, 99, 114, 120, 135, 141, 156, 174, 210, 216, 231, 261, 285, 300, 309, 321, 330, 405, 411, 414, 429, 441, 510, 516, 525, 531, 546, 576, 615, 639, 645, 651, 660, 714, 726, 741, 744, 804, 810, 834, 849, 861, 894
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OFFSET

1,1


COMMENTS

Intersection of A005097 and A006254.  Zak Seidov, Mar 18 2005
The only possible pairs for 2a(n)+/1 are prime/prime (this sequence), not prime/not prime (A104278), prime/notprime (A104279) and not prime/prime (A104280), ... this sequence + A104280 + A104279 + A104278 = the odd numbers.
These numbers are never k mod (2k+1) or (k+1) mod (2k+1) with 2k+1 < a(n).  Jon Perry, Sep 04 2012
Excluding the first term, all remaining terms have digital root 3, 6 or 9.  J. W. Helkenberg, Jul 24 2013
Positive numbers x such that the difference between x^2 and adjacent squares are prime (both x^2(x1)^2 and (x+1)^2x^2 are prime).  Doug Bell, Aug 21 2015
A260689(a(n),1) = A264526(a(n)) = 1.  Reinhard Zumkeller, Nov 17 2015


LINKS

T. D. Noe, Table of n, a(n) for n=1..10001


FORMULA

a(n) = A014574(n)/2 = A054735(n+1)/4 = A111046(n+1)/8.
For n>1, a(n) = 3*A002822(n1).  Jason Kimberley, Nov 06 2015


MAPLE

P := select(isprime, [$1..1789]): map(p>(p+1)/2, select(p>member(p+2, P), P)); # Peter Luschny, Mar 03 2011


MATHEMATICA

Select[Range[900], And @@ PrimeQ[{1, 1} + 2# ] &] (* Ray Chandler, Oct 12 2005 *)


PROG

(PARI) p=2; forprime(b=3, 1e4, if(bp==2, print1((p+1)/2", ")); p=b) \\ Altug Alkan, Nov 10 2015
(Haskell)
a040040 = flip div 2 . a014574  Reinhard Zumkeller, Nov 17 2015


CROSSREFS

Cf. A001359, A006512, A014574, A054735, A111046, A045753 (even terms halved), A002822 (terms divided by 3).
Cf. A221310.
Cf. A260689, A264526.
Sequence in context: A113808 A308870 A273371 * A168497 A256975 A239882
Adjacent sequences: A040037 A040038 A040039 * A040041 A040042 A040043


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Cino Hilliard, Oct 21 2002
Title corrected by Daniel Forgues, Jun 01 2009
Edited by Daniel Forgues, Jun 21 2009
Comment corrected by Daniel Forgues, Jul 12 2009


STATUS

approved



