A234011 The sums of 2 consecutive odious numbers (A000069).

3, 6, 11, 15, 19, 24, 27, 30, 35, 40, 43, 47, 51, 54, 59, 63, 67, 72, 75, 79, 83, 86, 91, 96, 99, 102, 107, 111, 115, 120, 123, 126, 131, 136, 139, 143, 147, 150, 155, 160, 163, 166, 171, 175, 179, 184, 187, 191, 195, 198, 203, 207, 211, 216, 219, 222, 227, 232, 235, 239, 243, 246

Offset: 1

Author

Gerasimov Sergey, Dec 27 2013

Keywords

• nonn
• easy
• base

Comments

The union of A131323(k) and (A225822(m)+(-1)^m).

All even numbers in this sequence are evil numbers (A001969).

It seems that A233388(n) = a(A091785(n)).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A000069, A003159 (indices of odd numbers in A234011), A036554 (indices of even numbers in A234011), A131323 (odd sums of 2 successive odious or 2 successive evil numbers), A233388 (odious numbers in A234011), A234431 (sums of 2 consecutive evil numbers), A017101, A091785, A225822, A227930, A233388.

Programs

Mathematica

Plus @@@ Partition[Select[Range[125], OddQ[DigitCount[#, 2][[1]]] &], 2, 1] (* Amiram Eldar, Jul 24 2023 *)

PARI

a(n)=4*n-hammingweight(n-1)%2-hammingweight(n)%2 \\ Charles R Greathouse IV, Dec 29 2013

Scheme

(define (A234011 n) (+ (A000069 n) (A000069 (+ n 1)))) ;; Antti Karttunen, Dec 29 2013

Formula

a(n) = A000069(n) + A000069(n + 1).

4n - 2 <= a(n) <= 4n. - Charles R Greathouse IV, Dec 29 2013

a(2n+1) = 8n + 3 = A017101(n). - Ralf Stephan, Dec 31 2013

Extensions

Terms recomputed and checked by Antti Karttunen, Dec 29 2013