A286535 Restricted growth sequence of A278535 (prime-signature of A253565).

1, 2, 2, 3, 2, 3, 4, 5, 2, 3, 4, 5, 4, 6, 6, 7, 2, 3, 4, 5, 4, 6, 6, 7, 4, 6, 8, 9, 6, 10, 9, 11, 2, 3, 4, 5, 4, 6, 6, 7, 4, 6, 8, 9, 6, 10, 9, 11, 4, 6, 8, 9, 8, 12, 12, 13, 6, 10, 12, 14, 9, 14, 13, 15, 2, 3, 4, 5, 4, 6, 6, 7, 4, 6, 8, 9, 6, 10, 9, 11, 4, 6, 8, 9, 8, 12, 12, 13, 6, 10, 12, 14, 9, 14, 13, 15, 4, 6, 8, 9, 8, 12, 12, 13, 8, 12, 16, 17, 12, 18

Offset: 0

Author

Antti Karttunen, May 17 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A046523, A253565, A286531, A286533, A286622.

Programs

PARI

rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,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])); }
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
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530.
A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));
A253560(n) = if(1==n, 1, (n*prime(A061395(n))));
A253565(n) = if(n<2,(1+n),if(!(n%2),A253550(A253565(n/2)),A253560(A253565((n-1)/2)))); \\ Would be better if memoized!
A278535(n) = A046523(A253565(n));
write_to_bfile(0,rgs_transform(vector(65538,n,A278535(n-1))),"b286535.txt");