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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.)