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%I #18 Jul 01 2018 16:30:02
%S 1,2,3,5,7,11,13,16,17,19,21,23,25,26,29,31,33,35,37,38,41,43,45,47,
%T 49,52,53,55,57,59,61,62,65,67,69,71,73,74,77,79,81,83,85,86,89,91,93,
%U 95,97,101,103,104,105,107,109,113,116,117,119,121,125,127,128,129
%N a(n) is the smallest number greater than a(n-1) that is coprime to the last four terms of the sequence, with a(1) = 1, a(2) = 2, a(3) = 3, and a(4) = 5.
%C Is a(n+1) - a(n) bounded?
%C For n < 10^7, the maximum value of a(n+1) - a(n) is 12. - _T. D. Noe_, May 14 2007
%C The first differences appear to be periodic with period 245589; this should lead to a proof that the first differences are bounded. If the pattern holds through a(189103530) then it is proved; it suffices to work mod 2310. - _Charles R Greathouse IV_, Dec 19 2011
%H T. D. Noe, <a href="/A062063/b062063.txt">Table of n, a(n) for n = 1..1000</a>
%o (PARI) { for (n=1, 1000, if (n>4, until (gcd(a, a1)==1 && gcd(a, a2)==1 && gcd(a, a3)==1 && gcd(a, a4)==1, a++); a4=a3; a3=a2; a2=a1; a1=a, if (n==1, a=a4=1, if (n==2, a=a3=2, if (n==3, a=a2=3, a=a1=5)))); write("b062063.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 31 2009
%Y Cf. A047255, A062062.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Jun 12 2001
%E Corrected and extended by _Dean Hickerson_, Jul 10 2001
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