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 A040976 a(n) = prime(n) - 2. 54
 0, 1, 3, 5, 9, 11, 15, 17, 21, 27, 29, 35, 39, 41, 45, 51, 57, 59, 65, 69, 71, 77, 81, 87, 95, 99, 101, 105, 107, 111, 125, 129, 135, 137, 147, 149, 155, 161, 165, 171, 177, 179, 189, 191, 195, 197, 209, 221, 225, 227, 231, 237, 239, 249, 255, 261 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Numbers n such that n! reduced mod (n+2) is 1. - Benoit Cloitre, Mar 11 2002 The first a(n) numbers starting from 2 are divisible by primes up to p(n-1). - Lekraj Beedassy, Jun 21 2006 The terms in this sequence are the cumulative sums of distances from one prime to another. For example for the distance from the first to 26th prime, 2 to 101, the cumulative sum of distances is 99, always the last prime, here 101, minus 2. - Enoch Haga, Apr 24 2006 The primes in this sequence are the initial primes of pairs of twin primes. - Sebastiao Antonio da Silva, Dec 21 2008 Note that many, but not all, of these numbers satisfy x such that x^(x+1) = 1 mod (x+2). The first exception is 339. - Thomas Ordowski, Nov 27 2013 If this sequence had an infinite number of primes, the twin prime conjecture would follow. Sequence holds all primes in A001359. - John W. Nicholson, Apr 14 2014 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 S. A. Khan, Primes in Geometric-Arithmetic Progression, arXiv preprint arXiv:1203.2083 [math.NT], 2012. FORMULA a(n) = A000040(n) - 2 = Sum_{i=1..n-1} A001223(i). For n > 2: A092953(a(n)) = 1. - Reinhard Zumkeller, Nov 10 2012 EXAMPLE a(13) = 39, because A000040(13) = 41. MAPLE seq(ithprime(n)-2, n=1..2000); # Muniru A Asiru, Jan 31 2018 MATHEMATICA Prime[Range]-2 (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *) PROG (Haskell) a040976 n = a000040 n - 2 a040976_list = map (subtract 2) a000040_list -- Reinhard Zumkeller, Feb 22 2012 (PARI) a(n)=prime(n)-2 \\ Charles R Greathouse IV, Nov 20 2012 (MAGMA) [NthPrime(n)-2: n in [1..60]]; // Vincenzo Librandi, Jan 31 2018 (GAP) Filtered([1..10^2], IsPrime)-2; # Muniru A Asiru, Jan 31 2018 CROSSREFS Cf. A000040, A001223, A014689, A014692. Sequence in context: A024896 A160771 A249426 * A268174 A166104 A164121 Adjacent sequences:  A040973 A040974 A040975 * A040977 A040978 A040979 KEYWORD nonn,nice,easy AUTHOR STATUS approved

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)