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 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 (list; graph; refs; listen; history; text; internal format)
 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-(x-1)^2 and (x+1)^2-x^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(n-1). - 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(b-p==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 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

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Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)