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

Author

Antti Karttunen, Oct 03 2017

Keywords

• nonn

Links

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

Crossrefs

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

Cf. also A289813, A289814, A290093, A290094.

Programs

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)))

Formula

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