The On-Line Encyclopedia of Integer Sequences (OEIS)

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A336472

Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336466(i) = A336466(j), for all i, j >= 1.
(history; published version)

#7 by Susanna Cuyler at Sat Jul 25 10:36:41 EDT 2020

STATUS

proposed

approved

#6 by Antti Karttunen at Fri Jul 24 16:03:20 EDT 2020

STATUS

editing

proposed

#5 by Antti Karttunen at Fri Jul 24 15:03:43 EDT 2020

COMMENTS

For all i, j: A336460(i) = A336460(j) => a(i) = a(j).

Discussion

Fri Jul 24

16:01

Antti Karttunen: Used as a filtering sequence, thus longish data section.

#4 by Antti Karttunen at Fri Jul 24 15:01:51 EDT 2020

LINKS

Antti Karttunen, <a href="/A336472/b336472.txt">Table of n, a(n) for n = 1..65537</a>

#3 by Antti Karttunen at Fri Jul 24 15:00:01 EDT 2020

CROSSREFS

Cf. also A336162, A336460, A336470, A336471, A336472, A336473.

#2 by Antti Karttunen at Fri Jul 24 13:14:41 EDT 2020

NAME

allocated Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336466(i) = A336466(j), for Antti Karttunenall i, j >= 1.

DATA

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

OFFSET

1,3

COMMENTS

Restricted growth sequence transform of the ordered pair [A278222(n), A336466(n)].

PROG

(PARI)

up_to = 65537;

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; };

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));

A000265(n) = (n>>valuation(n, 2));

A336466(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]-1))^f[k, 2])); };

Aux336472(n) = [A278222(n), A336466(n)];

v336472 = rgs_transform(vector(up_to, n, Aux336472(n)));

A336472(n) = v336472[n];

CROSSREFS

Cf. A278222, A336466.

Cf. A336460, A336470, A336471, A336472, A336473.

KEYWORD