A305978 Filter sequence combining prime signatures of n and 2n+1.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jun 15 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A286258.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

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

Programs

PARI

up_to = 65537;
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
Aux305978(n) = [A046523(n),A046523(n+n+1)];
v305978 = rgs_transform(vector(up_to,n,Aux305978(n)));
A305978(n) = v305978[n];