A305899 -id:A305899 - cp's OEIS frontend

A305898 Filter sequence combining prime signature of n (A046523) and similar signature (A284011) obtained when Stern polynomial B(n,x) is 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, 9, 4, 5, 6, 2, 10, 2, 11, 4, 4, 4, 12, 2, 4, 4, 8, 2, 10, 2, 6, 6, 4, 2, 13, 3, 14, 4, 6, 2, 8, 15, 8, 4, 4, 2, 16, 2, 4, 17, 18, 15, 10, 2, 6, 4, 10, 2, 19, 2, 4, 6, 6, 15, 10, 2, 13, 20, 4, 2, 16, 4, 4, 4, 8, 2, 16, 15, 6, 4, 4, 15, 21, 2, 6, 6, 22, 2, 10, 2, 8, 10

Offset: 1

Antti Karttunen, Jul 01 2018

nonn

Restricted growth sequence transform of ordered pair [A046523(n), A284011(n)].

For all i, j: a(i) = a(j) => A305892(i) = A305892(j).

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

Cf. A046523, A284011, A305892, A305899.

Cf. also A305790.

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 A003961
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));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux305898(n) = [A046523(n), A284011(n)];
v305898 = rgs_transform(vector(up_to, n, Aux305898(n)));
A305898(n) = v305898[n];

A331742 Lexicographically earliest infinite sequence such that a(i) = a(j) => A323901(i) = A323901(j) for all i, j.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 3, 4, 4, 1, 7, 5, 8, 3, 9, 6, 10, 2, 11, 3, 10, 4, 5, 4, 12, 1, 13, 7, 14, 5, 15, 8, 16, 3, 17, 9, 18, 6, 19, 10, 20, 2, 17, 11, 18, 3, 9, 10, 21, 4, 22, 5, 8, 4, 22, 12, 12, 1, 23, 13, 24, 7, 25, 14, 26, 5, 27, 15, 28, 8, 19, 16, 29, 3, 30, 17, 31, 9, 32, 18, 33, 6, 34, 19, 33, 10, 35, 20, 36, 2, 35, 17, 37, 11, 38, 18, 14, 3, 34

Offset: 0

Antti Karttunen, Feb 05 2020

Restricted growth sequence transform of function A323901(n) = A002487(A163511(n)).

Cf. A002487, A163511, A323901.

Cf. also A286378, A305899, A331743, A331744, A331745.

\\ Needs also code from A323901.
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; };
v331742 = rgs_transform(vector(1+up_to, n, A323901(n-1)));
A331742(n) = v331742[1+n];

a(2^n) = 1 for all n >= 0.

cp's OEIS Frontend

A305898 Filter sequence combining prime signature of n (A046523) and similar signature (A284011) obtained when Stern polynomial B(n,x) is factored over Z.

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