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

0,2

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to primorial base

Example

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.

Prog

(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];

Crossrefs

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

Sequence in context: A038388 A366392 A272573 * A332230 A319999 A083501

Adjacent sequences: A328474 A328475 A328476 * A328478 A328479 A328480

Keyword

nonn

Author

Antti Karttunen, Oct 19 2019

Status

approved