A305978 - OEIS

%I #8 Jun 16 2018 18:31:20

%S 1,2,2,3,2,4,5,6,7,8,2,9,10,4,4,11,5,12,5,12,4,13,2,14,15,4,16,17,2,

%T 18,19,20,4,8,4,21,19,8,4,22,2,23,5,12,17,8,5,24,25,12,4,26,2,27,8,27,

%U 8,13,5,28,5,29,12,30,4,23,31,12,4,23,5,32,19,4,12,33,8,18,5,34,35,36,2,28,13,4,13,37,2,38,8,17,8,39,4,40,41,12,12,42,5,23

%N Filter sequence combining prime signatures of n and 2n+1.

%C Restricted growth sequence transform of A286258.

%H Antti Karttunen, <a href="/A305978/b305978.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

%o Aux305978(n) = [A046523(n),A046523(n+n+1)];

%o v305978 = rgs_transform(vector(up_to,n,Aux305978(n)));

%o A305978(n) = v305978[n];

%Y Cf. A046523, A101296, A286258, A305810, A305973, A305977.

%Y Cf. A005384 (positions of 2's), A234095 (of 5's).

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 15 2018