A305431 Restricted growth sequence transform of A278222(A305295(n)), constructed from runlengths of 1-digits in base-3 representation of A245612(n).

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

Offset: 0

Author

Antti Karttunen, Jun 01 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A245612, A278222, A305295, A305296, A305432, A305433.

Cf. also A305301.

Programs

PARI

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
A305295(n) = A289813(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; };
v305431 = rgs_transform(vector(65538,n,A278222(A305295(n-1))));
A305431(n) = v305431[1+n];