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 A352501 a(n) is the distance from n to the nearest integer that can be added to n without carries in balanced ternary. 1
 0, 1, 1, 2, 1, 1, 2, 4, 4, 5, 4, 4, 2, 1, 1, 2, 4, 4, 5, 7, 10, 11, 13, 10, 11, 13, 13, 14, 13, 13, 11, 10, 13, 11, 10, 7, 5, 4, 4, 2, 1, 1, 2, 4, 4, 5, 7, 10, 11, 13, 10, 11, 13, 13, 14, 16, 19, 20, 22, 28, 29, 31, 31, 32, 34, 37, 38, 40, 28, 29, 31, 31, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..9841 Wikipedia, Balanced ternary FORMULA a(n) = 1 iff n > 0 and n belongs to A003462 or A007051. a(3*n) = 3*a(n)+1 for any n > 0. EXAMPLE For n = 7: - the numbers k around 7, alongside their distance to 7, balanced ternary expansion and whether they require carries when added to 7, are: k d bter(k) carries? -- - ------- -------- 3 4 10 no 4 3 11 yes 5 2 1TT yes 6 1 1T0 yes 7 0 1T1 yes 8 1 10T yes 9 2 100 yes 10 3 101 yes 11 4 11T yes - so a(7) = 4. PROG (PARI) ok(u, v) = { while (u && v, my (uu=[0, +1, -1][1+u%3], vv=[0, +1, -1][1+v%3]); if (abs(uu+vv)>1, return (0)); u=(u-uu)/3; v=(v-vv)/3); return (1) } a(n) = for (d=0, oo, if (ok(n, n-d) || ok(n, n+d), return (d))) CROSSREFS Cf. A003462, A007051, A059095, A353158. Sequence in context: A108746 A333270 A333272 * A119558 A333450 A210112 Adjacent sequences: A352498 A352499 A352500 * A352502 A352503 A352504 KEYWORD nonn,base AUTHOR Rémy Sigrist, Apr 28 2022 STATUS approved

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Last modified March 22 13:50 EDT 2023. Contains 361430 sequences. (Running on oeis4.)