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A328477 Lexicographically earliest infinite sequence such that a(i) = a(j) => A328469(A276086(i)) = A328469(A276086(j)) for all i, j. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A138221 A038388 A272573 * A319999 A083501 A007922

Adjacent sequences:  A328474 A328475 A328476 * A328478 A328479 A328480

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2019

STATUS

approved

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Last modified January 27 15:14 EST 2020. Contains 331295 sequences. (Running on oeis4.)