A305434 -id:A305434 - cp's OEIS frontend

A286531 Restricted growth sequence of A278531 (prime-signature of A163511).

1, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 7, 5, 5, 2, 8, 6, 9, 4, 10, 7, 7, 3, 9, 7, 11, 5, 7, 5, 5, 2, 12, 8, 13, 6, 14, 9, 9, 4, 14, 10, 15, 7, 10, 7, 7, 3, 13, 9, 15, 7, 15, 11, 11, 5, 9, 7, 11, 5, 7, 5, 5, 2, 16, 12, 17, 8, 18, 13, 13, 6, 19, 14, 20, 9, 14, 9, 9, 4, 18, 14, 21, 10, 21, 15, 15, 7, 14, 10, 15, 7, 10, 7, 7, 3, 17, 13, 20, 9, 21, 15, 15, 7, 20, 15

Offset: 0

Antti Karttunen, May 17 2017

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

Cf. A046523, A163511, A286533, A286535, A286219, A286622, A305433, A305434.

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])); }
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler
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
A278222(n) = A046523(A005940(1+n));
A054429(n) = ((3<<#binary(n\2))-n-1); \\ After M. F. Hasler, Aug 18 2014
A278531(n) = if(!n,1,A278222(A054429(n)));
write_to_bfile(0,rgs_transform(vector(65538,n,A278531(n-1))),"b286531.txt");

A285713 a(n) = A046523(A245612(n)).

Original entry on oeis.org

1, 2, 2, 2, 6, 2, 8, 4, 2, 12, 6, 4, 2, 12, 2, 6, 6, 2, 12, 12, 2, 6, 6, 2, 12, 24, 2, 6, 32, 12, 2, 2, 6, 6, 30, 2, 2, 210, 6, 60, 12, 2, 48, 24, 6, 6, 30, 6, 6, 30, 2, 120, 6, 2, 12, 72, 6, 30, 2, 6, 12, 6, 12, 4, 6, 6, 48, 60, 6, 60, 6, 2, 24, 192, 6, 6, 24, 768, 2, 6, 2, 6, 6, 6, 2, 30, 6, 210, 6, 6, 12, 48, 6, 12, 6, 6, 96, 12, 6, 30, 12, 12, 2, 2, 6

Offset: 0

Antti Karttunen, Apr 25 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A046523, A163511, A245612, A278224, A278531, A285712, A286613.

Cf. A305434 (rgs-transform).

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A254049(n) = A048673((2*n)-1);
A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A285713(n) = A046523(A245612(n)); \\ Antti Karttunen, Jun 01 2018

(define (A285713 n) (A046523 (A245612 n)))

a(n) = A046523(A245612(n)).
a(n) = A278224(A163511(n)).
a(n) = A286613(A054429(n)). - Antti Karttunen, Jun 01 2018

A305433 Restricted growth sequence transform of ordered pair [A278222(A305295(n)), A278222(A291763(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A245612(n).

Original entry on oeis.org

1, 2, 3, 1, 4, 5, 6, 7, 8, 3, 4, 9, 10, 2, 3, 2, 11, 12, 13, 14, 15, 8, 16, 10, 17, 14, 18, 5, 14, 19, 9, 3, 20, 21, 22, 23, 24, 25, 10, 16, 26, 27, 28, 29, 21, 10, 30, 31, 32, 29, 10, 19, 33, 15, 34, 6, 15, 14, 3, 14, 29, 3, 35, 1, 36, 37, 38, 39, 40, 21, 41, 42, 43, 44, 45, 27, 29, 46, 47, 48, 49, 50, 51, 50, 52, 53, 54, 55, 56, 10, 33, 33, 54, 10, 14

Offset: 0

Antti Karttunen, Jun 01 2018

nonn

Restricted growth sequence transform of A290093(A245612(n)).

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

Cf. A245612, A278222, A290093, A290094, A291763, A305295, A305431, A305432, A305434.

Cf. also A305303.

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A254049(n) = A048673((2*n)-1);
A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289813
A305295(n) = A289813(A245612(n));
A291763(n) = A289814(A245612(n));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
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; };
Aux305433(n) = [A278222(A305295(n)), A278222(A291763(n))];
v305433 = rgs_transform(vector(65538,n,Aux305433(n-1)));
A305433(n) = v305433[1+n];

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A286531 Restricted growth sequence of A278531 (prime-signature of A163511).

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A285713 a(n) = A046523(A245612(n)).

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A305433 Restricted growth sequence transform of ordered pair [A278222(A305295(n)), A278222(A291763(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A245612(n).

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PARI