A305899 Filter sequence related to factorization ("prime") signatures of Stern polynomials when factored over Z.

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

Offset: 1

Author

Antti Karttunen, Jul 01 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A284011.

Links

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

Crossrefs

Cf. A260443, A284011, A305898.

Cf. also A304751.

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; };
pfps(n) = { my(f=factor(n)); sum(i=1, #f~, f[i, 2] * 'x^(primepi(f[i, 1])-1)); };
A284010(n) = { if(!bitand(n, (n-1)), 0, my(p=0, f=vecsort(factor(pfps(n))[, 2], ,4)); prod(i=1, #f, (p=nextprime(p+1))^f[i])); }
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));
A284011(n) = A284010(A260443(n));
v305899 = rgs_transform(vector(up_to, n, A284011(n)));
A305899(n) = v305899[n];