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A305899 Filter sequence related to factorization ("prime") signatures of Stern polynomials when factored over Z. 3

%I #8 Jul 01 2018 08:35:53

%S 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,

%T 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,

%U 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

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

%C Restricted growth sequence transform of A284011.

%H Antti Karttunen, <a href="/A305899/b305899.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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; };

%o pfps(n) = { my(f=factor(n)); sum(i=1, #f~, f[i, 2] * 'x^(primepi(f[i, 1])-1)); };

%o 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])); }

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From _Michel Marcus_

%o A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));

%o A284011(n) = A284010(A260443(n));

%o v305899 = rgs_transform(vector(up_to, n, A284011(n)));

%o A305899(n) = v305899[n];

%Y Cf. A260443, A284011, A305898.

%Y Cf. also A304751.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 01 2018

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)