

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
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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(nk) and k + a(n1) not in A013929}. a(n) = MIN{k > 0 such that 3(nk) and k + a(n1) in A005117}.


MAPLE

S:= {0, 1}: mink:= 2: A[1]:= 1:
for n from 2 to 100 do
for k from mink + (nmink mod 3) by 3 do
if not member(k, S) and numtheory:issqrfree(A[n1]+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



