A353158 - OEIS

A353158

a(n) is the distance from n to the nearest integer that can be added to n without carries in base 3.

0, 0, 1, 0, 0, 2, 3, 2, 1, 0, 0, 1, 0, 0, 2, 4, 6, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 0, 0, 2, 3, 2, 1, 0, 0, 1, 0, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4

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OFFSET

0,6

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..9841

FORMULA

a(n) = 0 iff n belongs to A005836.

EXAMPLE

For n = 42:

- the numbers k around 42, alongside their distance to 42, ternary expansion and whether they require carries when added to 42, are:

k d ter(k) carries?

-- - ------ --------

38 4 1102 no

39 3 1110 yes

40 2 1111 yes

41 1 1112 yes

42 0 1120 yes

43 1 1121 yes

44 2 1122 yes

45 3 1200 yes

46 4 1201 yes

- so a(42) = 4.

PROG

(PARI) ok(u, v) = sumdigits(u+v, 3)==sumdigits(u, 3)+sumdigits(v, 3)

a(n) = { for (d=0, oo, if (ok(n, n-d) || ok(n, n+d), return (d))) }

CROSSREFS

Cf. A005836 (positions of zeros), A167877, A353157 (binary variant).

Sequence in context: A017878 A301572 A017868 * A334476 A319573 A178904

Adjacent sequences: A353155 A353156 A353157 * A353159 A353160 A353161

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Apr 27 2022

STATUS

approved