A115419 Numbers having a 1 in position 3 of their binary expansion.

8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 40, 41, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 63, 72, 73, 74, 75, 76, 77, 78, 79, 88, 89, 90, 91, 92, 93, 94, 95, 104, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127

Offset

1,1

Comments

One of the mystery calculator sequences: A005408, A042964, A047566, A115419, A115420, A115421.

Numbers congruent to {8,9,10,11,12,13,14,15} mod 16. Numbers n such that n xor 8 = n - 8. [Brad Clardy, May 06 2013]

Links

Table of n, a(n) for n=1..64.

Edd Mann, Mystery Calculator.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Formula

G.f.: -(x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+8)*x / (-x^9+x^8+x-1). - Alois P. Heinz, Aug 22 2011

Example

a(1) = 8 = 1000 in binary.

Maple

a:= n-> n+7 + 8*iquo(n-1, 8):
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 22 2011

Prog

(PARI) a(n)=(n-1)\8*16+(n-1)%8+8 \\ Charles R Greathouse IV, May 06 2013
(Python)
def A115419(n): return ((n-1<<1)&-7|8)+(n-1&7) # Chai Wah Wu, Mar 28 2024

Crossrefs

Cf. A005408, A042964, A047566, A115420, A115421.

Sequence in context: A089017 A182361 A023391 * A294238 A161639 A250044

Adjacent sequences: A115416 A115417 A115418 * A115420 A115421 A115422

Keyword

base,easy,nonn

Author

Jeremy Gardiner, Jan 22 2006

Status

approved