A270433 a(n) = number of terms A270431 <= n; least monotonic left inverse of A270431.

0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 16, 17, 18, 19, 19, 19, 19, 20, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 33, 34, 34, 34, 35, 35, 36, 37, 37, 37, 37, 38, 39, 39, 40, 41, 42

Offset

1,7

Links

Antti Karttunen, Table of n, a(n) for n = 1..35000

Formula

a(1) = 0, for n > 1, a(n) = (A048673(n)-A064216(n) reduced modulo 2)) + a(n-1).

Other identities. For all n >= 1:

a(n) = n - A270432(n).

a(A270431(n)) = n.

Mathematica

f[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; g[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1]; s = Select[Range@ 200, Xor[EvenQ@ f@ #, EvenQ@ g@ #] &] ; Table[Count[s, k_ /; k <= n], {n, 88}] (* Michael De Vlieger, Mar 17 2016 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A270433 n) (if (<= n 1) 0 (+ (modulo (- (A048673 n) (A064216 n)) 2) (A270433 (- n 1)))))

Crossrefs

Cf. A048673, A064216, A270431, A270432, A270434.

Sequence in context: A025775 A169993 A325620 * A169994 A169995 A213419

Adjacent sequences: A270430 A270431 A270432 * A270434 A270435 A270436

Keyword

nonn

Author

Antti Karttunen, Mar 17 2016

Status

approved