A328477 Lexicographically earliest infinite sequence such that a(i) = a(j) => A328469(A276086(i)) = A328469(A276086(j)) for all i, j.

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

Offset: 0

Author

Antti Karttunen, Oct 19 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of function f(n) = A328469(A276086(n)), or equally, of the function g(0) = 0; n > 0, g(n) = [A053669(n), A278226(n)], where in the ordered pair A053669(n) gives the smallest prime not dividing n, while A278226(n) gives the prime signature of A276086(n), i.e., a signature of the multiset of nonzero digits in the primorial base expansion of n. Note that A000720(A053669(n)) = A055396(A276086(n)) is one more than the number of trailing zeros in the primorial base expansion for n > 0.

Examples

			When written in primorial base (A049345), numbers 42 ("1200" as 42 = 1*A002110(3) + 2*A002110(2) + 0*A002110(1) + 0*A002110(0) = 1*30 + 2*6 + 0*2 + 0*1), 66 ("2100" as 66 = 2*30 + 1*6 + 0*2 + 0*1) and 222 ("10200" as 222 = 1*210 + 0*30 + 2*6 + 0*2 + 0*1) all have {1, 2} as their multiset of nonzero digits, and all have exactly two trailing zeros, thus they get an equal value in this sequence, namely a(42) = a(66) = a(222) = 33, where 33 is a running number allotted by the restricted growth sequence transform.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base

Crossrefs

Cf. A020639, A046523, A049345, A053669, A276086, A278226, A286626, A328399, A328469.

Programs

PARI

up_to = 32768;
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; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
Aux328469(n) = [A020639(n), A046523(n)];
Aux328477(n) = Aux328469(A276086(n));
v328477 = rgs_transform(vector(1+up_to, n, Aux328477(n-1)));
A328477(n) = v328477[1+n];