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A131485 Smallest positive integer k == n mod 3 not occurring earlier such that the sum of two successive terms is a squarefree number. 1
1, 2, 3, 4, 11, 6, 7, 8, 9, 10, 5, 12, 19, 14, 15, 16, 17, 18, 13, 20, 21, 22, 29, 24, 31, 26, 27, 28, 23, 30, 25, 32, 33, 34, 35, 36, 37, 41, 42, 40, 38, 39, 43, 44, 45, 46, 47, 48, 49, 53, 54, 52, 50, 51, 55, 56, 57, 58, 65, 66, 61, 62, 60, 67, 71, 63, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Mod 3 analog of A077223. A permutation of the natural numbers. There's an obvious limit to the number of successive values which can be consecutive integers.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = MIN{k > 0 such that 3|(n-k) and k + a(n-1) not in A013929}. a(n) = MIN{k > 0 such that 3|(n-k) and k + a(n-1) in A005117}.

MAPLE

S:= {0, 1}: mink:= 2: A[1]:= 1:

for n from 2 to 100 do

  for k from mink + (n-mink mod 3) by 3 do

    if not member(k, S) and numtheory:-issqrfree(A[n-1]+k) then

       A[n]:= k; S:= S union {k};

       if k = mink then mink := min({$mink .. max(S)+1} minus S) fi;

       break

    fi

  od

od:seq(A[i], i=1..100); # Robert Israel, Jun 19 2016

CROSSREFS

Cf. A005117, A013929, A077223.

Sequence in context: A265351 A065633 A160652 * A075833 A265904 A117351

Adjacent sequences:  A131482 A131483 A131484 * A131486 A131487 A131488

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Oct 01 2007

EXTENSIONS

Corrected and extended by Giovanni Resta, Jun 19 2016

STATUS

approved

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Last modified June 26 20:37 EDT 2019. Contains 324380 sequences. (Running on oeis4.)