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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A137613 Omit the 1's from Rowland's sequence f(n) - f(n-1) = gcd(n,f(n-1)), where f(1) = 7. 11
 5, 3, 11, 3, 23, 3, 47, 3, 5, 3, 101, 3, 7, 11, 3, 13, 233, 3, 467, 3, 5, 3, 941, 3, 7, 1889, 3, 3779, 3, 7559, 3, 13, 15131, 3, 53, 3, 7, 30323, 3, 60647, 3, 5, 3, 101, 3, 121403, 3, 242807, 3, 5, 3, 19, 7, 5, 3, 47, 3, 37, 5, 3, 17, 3, 199, 53, 3, 29, 3, 486041, 3, 7, 421, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Rowland proves that each term is prime. He says it is likely that all odd primes occur. In the first 5000 terms, there are 965 distinct primes and 397 is the least odd prime that does not appear. - T. D. Noe, Mar 01 2008 In the first 10000 terms, the least odd prime that does not appear is 587, according to Rowland. - Jonathan Sondow, Aug 14 2008 Removing duplicates from this sequence yields A221869. The duplicates are A225487. - Jonathan Sondow, May 03 2013 LINKS T. D. Noe, Table of n, a(n) for n = 1..5000 Jean-Paul Delahaye, Déconcertantes conjectures, Pour la science, 5 (2008), 92-97. Brian Hayes, Pumping the Primes, bit-player, 19 August 2015. John Moyer, Source code in C and C++ to print this sequence or sorted and unique values from this sequence. [From John Moyer (jrm(AT)rsok.com), Nov 06 2009] Ivars Peterson, A New Formula for Generating Primes, The Mathematical Tourist. Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc. 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986). Eric S. Rowland, A natural prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008. Eric S. Rowland, A natural prime-generating recurrence, J. of Integer Sequences 11 (2008), Article 08.2.8. Eric Rowland, A simple recurrence that produces complex behavior ..., A New Kind of Science blog. Eric Rowland, Prime-Generating Recurrence, Wolfram Demonstrations Project, 2008. Eric Rowland, A Bizarre Way to Generate Primes, YouTube video, 2023. Jeffrey Shallit, Rutgers Graduate Student Finds New Prime-Generating Formula, Recursivity blog. Vladimir Shevelev, Generalizations of the Rowland theorem, arXiv:0911.3491 [math.NT], 2009-2010. Wikipedia, Formula for primes. FORMULA Denote by Lpf(n) the least prime factor of n. Then a(n) = Lpf( 6-n+Sum_{i=1..n-1} a(i) ). - Vladimir Shevelev, Mar 03 2010 a(n) = A168008(2*n+4) (conjectured). - Jon Maiga, May 20 2021 a(n) = A020639(A190894(n)). - Seiichi Manyama, Aug 11 2023 EXAMPLE f(n) = 7, 8, 9, 10, 15, 18, 19, 20, ..., so f(n) - f(n-1) = 1, 1, 1, 5, 3, 1, 1, ... and a(n) = 5, 3, ... . From Vladimir Shevelev, Mar 03 2010: (Start) a(1) = Lpf(6-1) = 5; a(2) = Lpf(6-2+5) = 3; a(3) = Lpf(6-3+5+3) = 11; a(4) = Lpf(6-4+5+3+11) = 3; a(5) = Lpf(6-5+5+3+11+3) = 23. (End) MAPLE A137613_list := proc(n) local a, c, k, L; L := NULL; a := 7; for k from 2 to n do c := igcd(k, a); a := a + c; if c > 1 then L:=L, c fi; od; L end: A137613_list(500000); # Peter Luschny, Nov 17 2011 MATHEMATICA f[1] = 7; f[n_] := f[n] = f[n - 1] + GCD[n, f[n - 1]]; DeleteCases[Differences[Table[f[n], {n, 10^6}]], 1] (* Alonso del Arte, Nov 17 2011 *) PROG (Haskell) a137613 n = a137613_list !! (n-1) a137613_list = filter (> 1) a132199_list -- Reinhard Zumkeller, Nov 15 2013 (PARI) ub=1000; n=3; a=9; while(n 1: yield b a += b A137613_list = list(islice(A137613_gen(), 20)) # Chai Wah Wu, Mar 14 2023 CROSSREFS f(n) = f(n-1) + gcd(n, f(n-1)) = A106108(n) and f(n) - f(n-1) = A132199(n-1). Cf. also A084662, A084663, A134734, A134736, A134743, A134744, A221869. Cf. A020639, A168008, A190894, A231900. Sequence in context: A195140 A049829 A258333 * A335302 A259650 A165670 Adjacent sequences: A137610 A137611 A137612 * A137614 A137615 A137616 KEYWORD nonn AUTHOR Jonathan Sondow, Jan 29 2008, Jan 30 2008 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 November 30 19:18 EST 2023. Contains 367462 sequences. (Running on oeis4.)