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A286449 Restricted growth sequence computed for A033879 (deficiency), or equally, for A033880 (abundance of n). 8
1, 1, 2, 1, 3, 4, 5, 1, 6, 2, 7, 8, 9, 3, 5, 1, 10, 11, 12, 13, 7, 14, 15, 16, 17, 7, 18, 4, 19, 16, 20, 1, 12, 18, 15, 21, 22, 10, 15, 23, 24, 16, 25, 3, 9, 26, 27, 28, 29, 30, 20, 5, 31, 16, 32, 33, 34, 35, 36, 37, 38, 19, 15, 1, 27, 16, 39, 7, 25, 8, 40, 41, 42, 34, 35, 9, 36, 16, 43, 44, 29, 32, 45, 46, 47, 24, 48, 8, 49, 50, 40, 10, 36, 51, 40, 52, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sigma(n)

EXAMPLE

We start by setting a(1) = 1 for A033879(1) = 1. Then after, whenever A033879(k) is equal to some A033879(m) with m < k, we set a(k) = a(m). Otherwise, (when the value is a new one, not encountered before), we allot for a(k) the least natural number not present among a(1) .. a(k-1).

For n=2, as A033879(2) = 1, which was already present at A033879(1), we set a(2) = a(1) = 1.

For n=3, as A033879(3) = 2, which is a new value not encountered before, we set a(3) = 1 + max(a(1),a(2)) = 2.

For n=4, as A033879(4) = 1, which was already present at n = 2 and n = 1, we set a(4) = a(1) = 1.

For n=5, as A033879(5) = 4, which is a new value not encountered before, we set a(5) = 1 + max(a(1),a(2),a(3),a(4)) = 3.

For n=12, as A033879(12) = -4, which is a new value not encountered before, we set a(12) = 1 + max(a(1),...,a(11)) = 8. Note that the sign matters here, -4 is not equal to +4 which was encountered already at n=5.

PROG

(PARI)

rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences, invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences, invec[i], i); outvec[i] = u; u++ )); outvec; };

write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

A033879(n) = ((2*n)-sigma(n));

write_to_bfile(1, rgs_transform(vector(10000, n, A033879(n))), "b286449.txt");

CROSSREFS

Cf. A000203, A033879, A033880, A286448, A286450, A286603.

Sequence in context: A085985 A285107 A088267 * A284584 A256100 A117407

Adjacent sequences:  A286446 A286447 A286448 * A286450 A286451 A286452

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 13 2017

STATUS

approved

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Last modified August 19 13:00 EDT 2017. Contains 290807 sequences.