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A132199 Rowland's prime-generating sequence: first differences of A106108. 25
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. [From 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, ..., . [From 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, ..., . [From 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). [From 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 . [From Robert G. Wilson v, Apr 30 2009]

Eric S. Rowland, A simple prime-generating recurrence.

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 (* From 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

CROSSREFS

Cf. A106108, A137613. See A106108 for other cross-references.

Cf. A134734, A134743, A134744.

Sequence in context: A181886 A126853 A201654 * 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 April 17 11:46 EDT 2014. Contains 240635 sequences.