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A302780 Restricted growth sequence transform of 4-tuple [H(H(n-1)), H(n-H(n-1)), Q(n-Q(n-1)), Q(n-Q(n-2))] where H = A004001 and Q = A005185. 2
1, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 25, 25, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 37, 38, 38, 39, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 47, 50, 50, 50, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 79, 80, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Restricted growth sequence transform of A286560: a filter sequence which includes both the summands of A004001 and the summands of A005185.

For all i, j: a(i) = a(j) => b(i) = b(j), where b is a sequence like A087740, A284019, A286569 or A302779.

For n > 1000 the duplicates get rare. In range [1000, 65536] there are only three cases: a(1353) = a(1354) = 1319, a(39361) = a(39362) = 39326, and a(46695) = a(46696) = 46659.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for Hofstadter-type sequences

PROG

(PARI)

up_to = 65537;

first_n_of_A004001(n) = { my(v=vector(n)); v[1]=v[2]=1; for(k=3, n, v[k]=v[v[k-1]]+v[k-v[k-1]]); (v); }; \\ Charles R Greathouse IV, Feb 26 2017

v004001 = first_n_of_A004001(up_to);

A004001(n) = v004001[n];

first_n_of_A005185(n) = { my(v=vector(n)); v[1]=v[2]=1; for(k=3, n, v[k]=v[k-v[k-1]]+v[k-v[k-2]]); (v); }; \\

v005185 = first_n_of_A005185(up_to);

A005185(n) = v005185[n];

Aux302780(n) = if(n<3, 0, [A004001(A004001(n-1)), A004001(n-A004001(n-1)), A005185(n-A005185(n-1)), A005185(n-A005185(n-2))]);

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; };

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

write_to_bfile(1, rgs_transform(vector(up_to, n, Aux302780(n))), "b302780.txt");

CROSSREFS

Cf. A004001, A005185, A286560.

Cf. also A087740, A284019, A286541, A286569, A302779.

Sequence in context: A171970 A071377 A076946 * A064524 A153249 A097621

Adjacent sequences:  A302777 A302778 A302779 * A302781 A302782 A302783

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 27 2018

STATUS

approved

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Last modified September 30 12:21 EDT 2020. Contains 337439 sequences. (Running on oeis4.)