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

Author

Jeremy Gardiner, Jan 22 2006

Keywords

• base
• easy
• nonn

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]

Examples

			a(1) = 8 = 1000 in binary.
		

Links

• Edd Mann, Mystery Calculator.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Crossrefs

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

Programs

Maple

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

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

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