A270430 Numbers n such that A048673(n) and A064216(n) are of the same parity.

1, 2, 3, 4, 5, 8, 9, 10, 12, 13, 16, 17, 20, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 48, 49, 50, 52, 53, 58, 62, 64, 65, 68, 69, 74, 75, 77, 80, 81, 82, 85, 90, 93, 97, 98, 99, 100, 101, 102, 104, 105, 106, 108, 109, 111, 113, 114, 116, 117, 120, 121, 124, 125, 126, 128, 130, 132, 133, 136, 137, 139, 141, 144

Offset

1,2

Comments

See A270434 for the possible bias favoring this sequence over the complement A270431.

Links

Antti Karttunen, Table of n, a(n) for n = 1..17000

Formula

Other identities. For all n >= 1:

A270432(a(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]; Select[Range@ 144, Xor[EvenQ@ f@ #, OddQ@ g@ #] &] (* Michael De Vlieger, Mar 17 2016 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A270430 (ZERO-POS 1 1 (lambda (n) (- (A000035 (A048673 n)) (A000035 (A064216 n))))))

Crossrefs

Complement: A270431.

Left inverse: A270432.

Cf. A245449 (a subsequence).

Cf. A000035, A048673, A064216, A270434.

Cf. also A269860.

Sequence in context: A032901 A260113 A005792 * A318932 A259185 A102471

Adjacent sequences: A270427 A270428 A270429 * A270431 A270432 A270433

Keyword

nonn

Author

Antti Karttunen, Mar 17 2016

Status

approved