

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.


3



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
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OFFSET

0,3


COMMENTS

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


LINKS

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


EXAMPLE

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


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


PROG

(PARI) a(n, b=7) = fromdigits(apply(d > if (d<b/2, d, db), digits(n, b)), b) \\ Rémy 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


CROSSREFS

Cf. A007093, A117966, A309991.
Column k=3 of A319047.
Sequence in context: A285555 A078041 A154840 * A205102 A247108 A236439
Adjacent sequences: A309992 A309993 A309994 * A309996 A309997 A309998


KEYWORD

base,sign


AUTHOR

Jackson Haselhorst, Aug 26 2019


STATUS

approved



