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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 First appearance of k-th prime, k=0..: 1, 0, 5, 4, 104, 10, 116, 242878, 242819, 22, 243019, 3891770, 242867, ..., . - Robert G. Wilson v, Apr 30 2009 The number of different numbers in the first 10^k terms beginning with k=0: 1, 4, 7, 12, 15, 19, 30, >35, ..., . - Robert G. Wilson v, Apr 30 2009 Records in A132199: 1, 5, 11, 23, 47, 101, 233, 467, 941, 1889, 3779, 7559, 15131, 30323, 60647, 121403, 242807, 486041, 972533, 1945649, 3891467, 7783541, ..., (see A191304). - Robert G. Wilson v, Apr 30 2009 REFERENCES Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986). Jean-Paul Delahaye, Fascinantes conjectures, Pour la science (French edition of Scientific American), No. 5, 2008 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 . 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. 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 November 26 03:08 EST 2022. Contains 358353 sequences. (Running on oeis4.)