A293225 Compound filter: a(n) = P(A293224(n), A293223(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 2, 2, 5, 2, 8, 2, 12, 4, 13, 2, 32, 2, 40, 30, 33, 2, 59, 2, 58, 42, 69, 2, 143, 8, 80, 29, 83, 2, 178, 2, 197, 38, 96, 25, 239, 2, 100, 121, 163, 2, 221, 2, 202, 194, 103, 2, 448, 61, 365, 59, 245, 2, 333, 48, 576, 187, 256, 2, 720, 2, 278, 546, 718, 138, 606, 2, 503, 114, 1009, 2, 1101, 2, 437, 651, 678, 532, 831, 2, 1400, 172, 213, 2, 1508, 71, 500, 597

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..19683

Formula

a(n) = (1/2)*(2 + ((A293224(n) + A293223(n))^2) - A293224(n) - 3*A293223(n)).

Prog

(PARI)
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; };
A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler
A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); };
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
A293221(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A289813(d)))); m; };
A293222(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A289814(d)))); m; };
v293223 = rgs_transform(vector(19683, n, A293221(n)));
A293223(n) = v293223[n];
v293224 = rgs_transform(vector(19683, n, A293222(n)));
A293224(n) = v293224[n];
A293225(n) = (1/2)*(2 + ((A293224(n) + A293223(n))^2) - A293224(n) - 3*A293223(n));
(Scheme) (define (A293225 n) (* 1/2 (+ (expt (+ (A293224 n) (A293223 n)) 2) (- (A293224 n)) (- (* 3 (A293223 n))) 2)))

Crossrefs

Cf. A000027, A019565, A293221, A293222, A293223, A293224, A293226 (rgs-version of this filter).

Cf. also A289813, A289814, A290093, A290094.

Sequence in context: A030996 A368580 A309208 * A353851 A305798 A305808

Adjacent sequences: A293222 A293223 A293224 * A293226 A293227 A293228

Keyword

nonn

Author

Antti Karttunen, Oct 03 2017

Status

approved