A270432 a(n) = number of terms A270430 <= n; least monotonic left inverse of A270430.

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

Offset

1,2

Links

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

Formula

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

Other identities. For all n >= 1:

a(n) = n - A270433(n).

a(A270430(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@ 144, Xor[EvenQ@ f@ #, OddQ@ g@ #] &]; Table[Count[s, k_ /; k <= n], {n, 84}] (* Michael De Vlieger, Mar 17 2016 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A270432 n) (if (<= n 1) n (+ (- 1 (modulo (- (A048673 n) (A064216 n)) 2)) (A270432 (- n 1)))))

Crossrefs

Cf. A270430, A270433, A270434.

Sequence in context: A349481 A200262 A347762 * A007599 A330881 A279317

Adjacent sequences: A270429 A270430 A270431 * A270433 A270434 A270435

Keyword

nonn

Author

Antti Karttunen, Mar 17 2016

Status

approved