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

1,2

Comments

Restricted growth sequence transform of A284011.

Links

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

Prog

(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];

Crossrefs

Cf. A260443, A284011, A305898.

Cf. also A304751.

Sequence in context: A338138 A384812 A369760 * A101296 A305898 A181819

Adjacent sequences: A305896 A305897 A305898 * A305900 A305901 A305902

Keyword

nonn

Author

Antti Karttunen, Jul 01 2018

Status

approved