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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<ub, d=gcd(n, a); print1(d, ", "); a=a+d; n=n+1; ); \\ Daniel Constantin Mayer, Aug 31 2014

CROSSREFS

Cf. A106108, A137613, A134734, A134743, A134744, A247090. See A106108 for other cross-references.

Sequence in context: A286127 A201654 A265606 * A111142 A179626 A174965

Adjacent sequences:  A132196 A132197 A132198 * A132200 A132201 A132202

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 28 2008

STATUS

approved

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Last modified November 26 03:08 EST 2022. Contains 358353 sequences. (Running on oeis4.)