The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001043 Numbers that are the sum of 2 successive primes. (Formerly M3780 N0968) 164
 5, 8, 12, 18, 24, 30, 36, 42, 52, 60, 68, 78, 84, 90, 100, 112, 120, 128, 138, 144, 152, 162, 172, 186, 198, 204, 210, 216, 222, 240, 258, 268, 276, 288, 300, 308, 320, 330, 340, 352, 360, 372, 384, 390, 396, 410, 434, 450, 456, 462, 472, 480, 492, 508, 520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Arithmetic derivative (see A003415) of prime(n)*prime(n+1). - Giorgio Balzarotti, May 26 2011 A008472(a(n)) = A191583(n). - Reinhard Zumkeller, Jun 28 2011 With the exception of the first term, all terms are even. a(n) is divisible by 4 if the difference between prime(n) and prime(n + 1) is not divisible by 4; e.g., prime(n) = 1 mod 4 and prime(n + 1) = 3 mod 4. In general, for a(n) to be divisible by some even number m > 2 requires that prime(n + 1) - prime(n) not be a multiple of m. - Alonso del Arte, Jan 30 2012 REFERENCES Archimedeans Problems Drive, Eureka, 26 (1963), 12. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe) Albert Frank & Philippe Jacqueroux, International Contest, 2001. Item 22 Richard K. Guy, Letters to N. J. A. Sloane, June-August 1968 Neil Sloane and Brady Haran, Eureka Sequences, Numberphile video (2021) FORMULA a(n) = prime(n) + prime(n + 1). a(n) = A000040(n) + A000040(n+1). a(n) = A116366(n, n - 1) for n > 1. - Reinhard Zumkeller, Feb 06 2006 EXAMPLE 2 + 3 = 5. 3 + 5 = 8. 5 + 7 = 12. 7 + 11 = 18. MAPLE Primes:= select(isprime, [2, seq(2*i+1, i=1..1000)]): n:= nops(Primes): Primes[1..n-1] + Primes[2..n]; # Robert Israel, Aug 29 2014 MATHEMATICA Table[Prime[n] + Prime[n + 1], {n, 55}] (* Ray Chandler, Feb 12 2005 *) Total/@Partition[Prime[Range[60]], 2, 1] (* Harvey P. Dale, Aug 23 2011 *) Abs[Differences[Table[(-1)^n Prime[n], {n, 60}]]] (* Alonso del Arte, Feb 03 2016 *) PROG (Sage) BB = primes_first_n(56) L = [] for i in range(55): L.append(BB[1 + i] + BB[i]) L # Zerinvary Lajos, May 14 2007 (Magma) [(NthPrime(n+1) + NthPrime(n)): n in [1..100]]; // Vincenzo Librandi, Apr 02 2011 (PARI) p=2; forprime(q=3, 1e3, print1(p+q", "); p=q) \\ Charles R Greathouse IV, Jun 10 2011 (PARI) is(n)=precprime((n-1)/2)+nextprime(n/2)==n&&n>2 \\ Charles R Greathouse IV, Jun 21 2012 (Haskell) a001043 n = a001043_list !! (n-1) a001043_list = zipWith (+) a000040_list \$ tail a000040_list -- Reinhard Zumkeller, Oct 19 2011 CROSSREFS Subsequence of A050936. Cf. A000040 (primes), A031131 (first differences). Sequence in context: A360404 A362243 A069102 * A118775 A025001 A020749 Adjacent sequences: A001040 A001041 A001042 * A001044 A001045 A001046 KEYWORD nonn,nice,easy AUTHOR N. J. A. Sloane, R. K. Guy EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Mar 17 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 13:14 EST 2023. Contains 367591 sequences. (Running on oeis4.)