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A084385 a(1) = 1; a(n+1) is the smallest number not occurring earlier and coprime to sum(j=1,n, a(j)). 3
1, 2, 4, 3, 7, 5, 9, 6, 8, 11, 13, 10, 12, 15, 17, 14, 16, 19, 21, 18, 20, 23, 25, 22, 24, 27, 29, 26, 28, 31, 33, 30, 32, 35, 37, 34, 36, 39, 41, 38, 40, 43, 45, 42, 44, 47, 49, 46, 48, 51, 53, 50, 52, 55, 57, 54, 56, 59, 61, 58, 60, 63, 65, 62, 64, 67, 69, 66, 68, 71, 73, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Rearrangement of the positive integers.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

FORMULA

For n > 6: a(n) = n - 2 for (n mod 4) = 0, a(n) = n - 1 for (n mod 4) = 1, a(n) = n + 1 for (n mod 4) = 2, a(n) = n + 2 for (n mod 4) = 3. - Klaus Brockhaus, Nov 30 2003.

EXAMPLE

1+2+4 = 7, 3 is the smallest number not occurring earlier and coprime to 7, hence a(4) = 3.

PROG

(PARI) used(k, v)=b=0; j=1; while(b<1&&j<=length(v), if(v[j]==k, b=1, j++)); b

{print1(s=1, ", "); v=[s]; for(n=1, 72, j=1; k=2; while(used(k, v)||gcd(k, s)>1, k++); v=concat(v, k); s=s+k; print1(k, ", "))}

(PARI) {print1(1, ", ", 2, ", ", 4, ", ", 3, ", ", 7, ", ", 5, ", "); for(n=7, 73, m=n%4; d=(if(m==0, -2, if(m==1, -1, if(m==2, 1, 2)))); print1(n+d, ", "))}

(Haskell)

import Data.List (delete)

a084385 n = a084385_list !! (n-1)

a084385_list = 1 : f [2..] 1 where

   f xs s = g xs where

     g (y:ys) = if gcd s y == 1 then y : f (delete y xs) (s + y) else g ys

-- Reinhard Zumkeller, Aug 15 2015

CROSSREFS

Partial sums are in A111244. Cf. A064413.

Cf. A261351 (inverse).

Sequence in context: A215673 A120619 A346298 * A073885 A256283 A257465

Adjacent sequences:  A084382 A084383 A084384 * A084386 A084387 A084388

KEYWORD

nonn

AUTHOR

Amarnath Murthy, May 29 2003

EXTENSIONS

Edited, corrected and extended by Klaus Brockhaus, May 29 2003

STATUS

approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)