A309995 Balanced septenary enumeration (or balanced septenary representation) of integers; write n in septenary and then replace 4's with (-3),s, 5's with (-2)'s, and 6's with (-1)'s.

0, 1, 2, 3, -3, -2, -1, 7, 8, 9, 10, 4, 5, 6, 14, 15, 16, 17, 11, 12, 13, 21, 22, 23, 24, 18, 19, 20, -21, -20, -19, -18, -24, -23, -22, -14, -13, -12, -11, -17, -16, -15, -7, -6, -5, -4, -10, -9, -8, 49, 50, 51, 52, 46, 47, 48, 56, 57, 58, 59, 53, 54, 55, 63

Offset: 0

Author

Jackson Haselhorst, Aug 26 2019

Keywords

• base
• sign

Comments

This sequence, like the balanced ternary and quinary sequences, includes every integer exactly once.

Examples

			As 54_10 = 105_7, the digits of 54 in base 7 are 1, 0 and 5. 5 > 3 so it's replaced by -2. The digits then are 1, 0 and -2 giving a(54) = 1*7^2 + 0 * 7^1 + (-2) * 7^0 = 49 + 0 - 2 = 47. - _David A. Corneth_, Aug 26 2019
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..16806

Crossrefs

Cf. A007093, A117966, A309991.

Column k=3 of A319047.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      7*a(iquo(n, 7))+mods(n, 7))
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Aug 26 2019

PARI

a(n,b=7) = fromdigits(apply(d -> if (dRémy Sigrist, Aug 26 2019

PARI

a(n) = my(d = digits(n, 7)); for(i = 1, #d, if(d[i] > 3, d[i]-=7)); fromdigits(d, 7) \\ David A. Corneth, Aug 26 2019