A286559 -id:A286559 - cp's OEIS frontend

A286560 Compound filter (summands of A004001 & summands of A005185): a(n) = P(A286541(n), A286559(n)), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

0, 0, 1, 2, 5, 41, 71, 71, 198, 313, 484, 922, 1153, 1201, 2105, 1565, 2588, 4046, 5001, 7443, 7443, 8851, 10671, 19589, 16570, 16935, 22254, 25313, 25313, 25313, 42891, 28793, 32768, 52795, 65504, 59178, 73355, 89033, 88632, 107660, 129045, 129045, 153471, 167646, 167646, 182446, 182446, 336130, 197244, 233297, 330472, 307358, 270167, 355325, 378466, 332156

Offset: 1

Antti Karttunen, May 18 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A004001, A005185, A284019, A286541, A286559, A286569.

(define (A286560 n) (if (<= n 2) 0 (* (/ 1 2) (+ (expt (+ (A286541 n) (A286559 n)) 2) (- (A286541 n)) (- (* 3 (A286559 n))) 2))))

a(1) = a(2) = 0, for n > 2, a(n) = (1/2)*(2 + ((A286541(n)+A286559(n))^2) - A286541(n) - 3*A286559(n)).

A286541 Compound filter (the left & right summand of Hofstadter-Conway $10000 sequence): a(n) = P(A004001(A004001(n-1)), A004001(n-A004001(n-1))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

Original entry on oeis.org

0, 0, 1, 1, 2, 5, 5, 5, 8, 13, 19, 19, 25, 25, 25, 25, 32, 41, 51, 62, 62, 73, 86, 86, 99, 99, 99, 113, 113, 113, 113, 113, 128, 145, 163, 182, 202, 202, 222, 244, 267, 267, 290, 315, 315, 340, 340, 340, 366, 394, 394, 422, 422, 422, 451, 451, 451, 451, 481, 481, 481, 481, 481, 481, 512, 545, 579, 614, 650, 687, 687, 724, 763, 803, 844, 844, 885, 928, 972, 972

Offset: 1

Antti Karttunen, May 18 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A004001, A286559, A286560.

Cf. A283468, A283469, A283470, A283472 and also A283471, A283473.

(define (A286541 n) (if (<= n 2) 0 (* (/ 1 2) (+ (expt (+ (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1))))) 2) (- (A004001 (A004001 (- n 1)))) (- (* 3 (A004001 (- n (A004001 (- n 1)))))) 2))))

a(1) = a(2) = 0, for n > 2, a(n) = (1/2)*(2 + ((A004001(A004001(n-1))+A004001(n-A004001(n-1)))^2) - A004001(A004001(n-1)) - 3*A004001(n-A004001(n-1))).

A302779 Restricted growth sequence transform of ordered pair [Q(n-Q(n-1)), Q(n-Q(n-2))], the left & right summand of Hofstadter Q-sequence A005185.

Original entry on oeis.org

1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 7, 8, 7, 9, 10, 9, 11, 11, 12, 12, 12, 12, 13, 14, 15, 13, 13, 13, 13, 16, 17, 18, 16, 19, 20, 21, 22, 19, 22, 23, 23, 24, 24, 24, 24, 24, 25, 26, 27, 28, 29, 30, 31, 28, 32, 25, 28, 25, 25, 25, 25, 33, 34, 35, 36, 37, 38, 39, 33, 40, 36, 41, 42, 43, 39, 44, 43, 45, 46, 47, 48, 48, 49, 50, 51, 52, 52, 49, 53, 53, 53, 53, 53, 53

Offset: 1

Antti Karttunen, Apr 27 2018

nonn

Restricted growth sequence transform of A286559.

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for Hofstadter-type sequences

Cf. A005185, A286559, A302780.

up_to = 65537;
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];
Aux302779(n) = if(n<3,0,[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,Aux302779(n))),"b302779.txt");

cp's OEIS Frontend

A286560 Compound filter (summands of A004001 & summands of A005185): a(n) = P(A286541(n), A286559(n)), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

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A286541 Compound filter (the left & right summand of Hofstadter-Conway $10000 sequence): a(n) = P(A004001(A004001(n-1)), A004001(n-A004001(n-1))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

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A302779 Restricted growth sequence transform of ordered pair [Q(n-Q(n-1)), Q(n-Q(n-2))], the left & right summand of Hofstadter Q-sequence A005185.

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