cp's OEIS Frontend

A291769 Restricted growth sequence transform of A292249; filter combining multiplicative order of 2 mod 2n+1 & prime signature of 2n+1 (A002326 & A278223).

%I A291769 #9 Oct 02 2017 18:58:34
%S A291769 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,18,20,21,22,23,24,25,
%T A291769 26,27,28,29,30,31,18,32,33,34,35,36,37,38,39,40,25,41,12,18,17,42,43,
%U A291769 44,45,46,47,48,19,42,15,49,22,50,51,27,52,53,54,55,28,56,57,58,59,60,41,61,62,63,64,27,26,65,66,67,68,69,70,71,72,73,74,75,76,60,42
%N A291769 Restricted growth sequence transform of A292249; filter combining multiplicative order of 2 mod 2n+1 & prime signature of 2n+1 (A002326 & A278223).
%C A291769 Also restricted growth sequence transform of the odd bisection of A286573.
%H A291769 Antti Karttunen, <a href="/A291769/b291769.txt">Table of n, a(n) for n = 0..32768</a>
%o A291769 (PARI)
%o A291769 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A291769 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A291769 A002326(n) = if(n<0, 0, znorder(Mod(2, 2*n+1))); \\ This function from _Michael Somos_, Mar 31 2005
%o A291769 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011
%o A291769 A292249(n) = (1/2)*(2 + ((A002326(n)+A046523(n+n+1))^2) - A002326(n) - 3*A046523(n+n+1));
%o A291769 write_to_bfile(0,rgs_transform(vector(32769,n,A292249(n-1))),"b291769_upto32768.txt");
%Y A291769 Cf. A002326, A046523, A278223, A286573, A291766, A292249.
%Y A291769 Cf. A291766, A292267 for related filters.
%K A291769 nonn
%O A291769 0,2
%A A291769 _Antti Karttunen_, Oct 02 2017