A304105 Restricted growth sequence transform of A304104, a filter sequence related to how the divisors of n are expressed in Fibonacci number system.

1, 2, 2, 3, 2, 4, 5, 6, 7, 4, 5, 8, 2, 9, 4, 10, 11, 12, 11, 8, 6, 9, 13, 14, 15, 4, 16, 17, 5, 18, 11, 8, 19, 20, 9, 21, 13, 22, 4, 23, 11, 24, 25, 26, 27, 28, 5, 29, 30, 31, 32, 8, 33, 34, 6, 35, 36, 9, 11, 37, 25, 22, 12, 38, 39, 40, 33, 41, 16, 42, 25, 43, 11, 44, 45, 46, 47, 18, 11, 48, 49, 50, 51, 52, 53, 54, 19, 55, 2, 56, 9, 57, 22, 9, 58, 59, 13, 60

Offset: 1

Author

Antti Karttunen, May 13 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A005086, A304096, A300837, A304101, A304103, A304104.

Programs

PARI

\\ Needs also code from A304101:
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; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A304104(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(A304101(d)-1))); (m); };
write_to_bfile(1,rgs_transform(vector(up_to,n,A304104(n))),"b304105.txt");

Formula

For all i, j: a(i) = a(j) => b(i) = b(j), where b can be any of {A000005, A005086, A304096 or A300837} for example.