A374201 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A048679(A328845(i))) = A278222(A048679(A328845(j))), for all i, j >= 1, where A328845 is a Fibonacci-based variant of the arithmetic derivative.

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

Offset

0,3

Comments

Restricted growth sequence transform of A278222(A048679(A328845(n))), or equally, of A304101(A328845(n)).

Related to the Zeckendorf-representation (A014417) of A328845(n).

For all i, j >= 0: a(i) = a(j) => A328847(i) = A328847(j).

Links

Antti Karttunen, Table of n, a(n) for n = 0..75025

Prog

(PARI)
up_to = 75025;
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; };
A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
A003714(n) = { my(s=0, w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); }
A106151(n) = { my(s=0, i=0); while(n, if(2!=(n%4), s += (n%2)<<i; i++); n >>= 1); (s); };
A048679(n) = if(!n, n, A106151(2*A003714(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]); };
A278222(n) = A046523(A005940(1+n));
A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i, 1])/f[i, 1]));
v374201 = rgs_transform(vector(1+up_to, n, A278222(A048679(A328845(n-1)))));
A374201(n) = v374201[1+n];

Crossrefs

Cf. A000045, A014417, A048679, A278222, A304101, A328845, A328847.

Cf. also A304105, A373982.

Sequence in context: A329045 A329345 A054030 * A336311 A339874 A134740

Adjacent sequences: A374198 A374199 A374200 * A374202 A374203 A374204

Keyword

nonn

Author

Antti Karttunen, Jul 02 2024

Status

approved