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A053669 Smallest prime not dividing n. 37
2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Smallest prime coprime to n.

Smallest k >= 2 coprime to n.

a(#(p-1)) = a(A034386(p-1)) = p is the first appearance of prime p in sequence.

a(A005408(n)) = 2; for n > 2: a(n) = A112484(n,1). - Reinhard Zumkeller, Sep 23 2011

Average value is 2.920050977316134... - Charles R Greathouse IV, Nov 02 2013

Differs from A236454, "smallest number not dividing n^2", for the first time at n=210, where a(210)=11 while A236454(210)=8. A235921 lists all n for which a(n) differs from A236454. - Antti Karttunen, Jan 26 2014

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Igor Rivin, Geodesics with one self-intersection, and other stories

FORMULA

a(n) = A071222(n-1)+1. [Because the right hand side computes the smallest k >= 2 such that gcd(n,k) = gcd(n-1,k-1) which is equal to the smallest k >= 2 coprime to n] - Antti Karttunen, Jan 26 2014

EXAMPLE

a(60) = 7, since all primes smaller than 7 divide 60 but 7 does not.

MATHEMATICA

Table[k := 1; While[Not[GCD[n, Prime[k]] == 1], k++ ]; Prime[k], {n, 1, 60}] - Stefan Steinerberger, Apr 01 2006

With[{prs=Prime[Range[10]]}, Flatten[Table[Select[prs, !Divisible[ n, #]&, 1], {n, 110}]]] (* From Harvey P. Dale, May 03 2012 *)

PROG

(Haskell)

a053669 n = head $ dropWhile ((== 0) . (mod n)) a000040_list

-- Reinhard Zumkeller, Nov 11 2012

(PARI) a(n)=forprime(p=2, , if(n%p, return(p))) \\ Charles R Greathouse IV, Nov 20 2012

(Scheme) (define (A053669 n) (let loop ((i 1)) (cond ((zero? (modulo n (A000040 i))) (loop (+ i 1))) (else (A000040 i))))) ;; Antti Karttunen, Jan 26 2014

CROSSREFS

One more than A071222(n-1).

Cf. also A053670-A053674, A055874, A071222, A235921, A236454.

Cf. A079578, A087560, A096014.

Sequence in context: A087242 A123556 A236454 * A112047 A112048 A060395

Adjacent sequences:  A053666 A053667 A053668 * A053670 A053671 A053672

KEYWORD

nonn,nice,easy

AUTHOR

Henry Bottomley, Feb 15 2000

EXTENSIONS

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000 and James A. Sellers, Feb 22 2000.

Entry revised by David W. Wilson, Nov 25 2006

STATUS

approved

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Last modified November 21 11:17 EST 2014. Contains 249777 sequences.