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 A132199 Rowland's prime-generating sequence: first differences of A106108. 27
 1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 47, 3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 101, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Rowland shows that the terms are all 1's or primes. The prime terms form A137613. See A137613 for additional comments, links and references. - Jonathan Sondow, Aug 14 2008 From Robert G. Wilson v, Apr 30 2009: (Start) First appearance of k-th prime, k >= 0: 1, 0, 5, 4, 104, 10, 116, 242878, 242819, 22, 243019, 3891770, 242867, ..., . The number of different numbers in the first 10^k terms beginning with k=0: 1, 4, 7, 12, 15, 19, 30, >35, ..., . Record high values are A191304. (End) REFERENCES Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986). LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 . Jean-Paul Delahaye, Déconcertantes conjectures, Pour la Science (French edition of Scientific American), No. 367, May 2008. Brian Hayes, Pumping the Primes, bit-player, 19 August 2015. Eric S. Rowland, A natural prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008. Eric S. Rowland, A simple prime-generating recurrence, 2008. Eric S. Rowland, Prime-Generating Recurrences and a Tale of Logarithmic Scale, 20 January 2023. MAPLE A106108 := proc(n) option remember; if n = 1 then 7; else procname(n-1)+igcd(n, procname(n-1)) ; end if; end proc: A132199 := proc(n) A106108(n+1)-A106108(n) ; end proc: # R. J. Mathar, Jul 04 2013 MATHEMATICA a[1] = 7; a[n_] := a[n] = a[n - 1] + GCD[n, a[n - 1]]; t = Array[a, 104]; Rest@t - Most@t (* Robert G. Wilson v, Apr 30 2009 *) PROG (Haskell) a132199 n = a132199_list !! (n-1) a132199_list = zipWith (-) (tail a106108_list) a106108_list -- Reinhard Zumkeller, Nov 15 2013 (PARI) ub=1000; a=7; n=2; while(n

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Last modified August 10 05:42 EDT 2024. Contains 375044 sequences. (Running on oeis4.)