All confirmed. On Thu, Dec 15, 2011 at 2:25 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Confirmations appreciated.
a(1) = 10 a(2) = 45 a(3) = 10 a(4) = 23 a(5) = 18 a(6) = 15 a(7) = 10 a(8) = 12 a(9) = 10 a(10) = 9 a(11) = 10 a(12) = 13 a(13) = 8 a(14) = 17 a(15) = 12 a(16) = 16 a(17) = 7 a(18) = 5 a(19) = 10 a(20) = 45 a(21) = 9 a(22) = 9 a(23) = 9 a(24) = 19 a(25) = 36 a(26) = 15 a(27) = 7 a(28) = 17 a(29) = 7 a(30) = 9 a(31) = 10 a(32) = 18 a(33) = 10 a(34) = 27 a(35) = 16 a(36) = 11 a(37) = 10 a(38) = 5 a(39) = 10 a(40) = 23 a(41) = 9 a(42) = 9 a(43) = 7 a(44) = 9 a(45) = 8 a(46) = 11 a(47) = 10 a(48) = 12 a(49) = 10 a(50) = 18 a(51) = 9 a(52) = 18 a(53) = 8 a(54) = 11 a(55) = 9 a(56) = 12 a(57) = 10 a(58) = 5 a(59) = 10 a(60) = 15 a(61) = 9 a(62) = 9 a(63) = 8 a(64) = 9 a(65) = 11 a(66) = 11 a(67) = 7 a(68) = 14 a(69) = 5 a(70) = 8 a(71) = 10 a(72) = 11 a(73) = 10 a(74) = 7 a(75) = 12 a(76) = 12 a(77) = 7 a(78) = 5 a(79) = 10 a(80) = 12 a(81) = 9 a(82) = 7 a(83) = 10 a(84) = 11 a(85) = 8 a(86) = 11 a(87) = 7 a(88) = 9 a(89) = 9 a(90) = 5 a(91) = 10 a(92) = 6 a(93) = 10 a(94) = 6 a(95) = 7 a(96) = 6 a(97) = 10 a(98) = 8 a(99) = 10 a(100) = 9 a(101) = 9 a(102) = 9 a(103) = 7 a(104) = 9 a(105) = 9 a(106) = 9 a(107) = 7 a(108) = 9 a(109) = 5 a(110) = 9 a(111) = 10 a(112) = 8 a(113) = 8 a(114) = 7 a(115) = 7 a(116) = 11 a(117) = 7 a(118) = 5 a(119) = 9 a(120) = 13 a(121) = 8 a(122) = 8 a(123) = 9 a(124) = 19 a(125) = 72 a(126) = 15 a(127) = 7 a(128) = 7 a(129) = 7 a(130) = 8 a(131) = 8 a(132) = 6 a(133) = 8 a(134) = 7 a(135) = 7 a(136) = 7 a(137) = 8 a(138) = 5 a(139) = 10 a(140) = 17 a(141) = 7 a(142) = 8 a(143) = 7 a(144) = 9 a(145) = 8 a(146) = 5 a(147) = 8 a(148) = 7 a(149) = 7 a(150) = 12 a(151) = 8 a(152) = 6 a(153) = 6 a(154) = 6 a(155) = 7 a(156) = 6 a(157) = 7 a(158) = 5 a(159) = 10 a(160) = 16 a(161) = 7 a(162) = 9 a(163) = 8 a(164) = 9 a(165) = 15 a(166) = 33 a(167) = 7 a(168) = 19 a(169) = 8 a(170) = 7 a(171) = 7 a(172) = 11 a(173) = 6 a(174) = 5 a(175) = 15 a(176) = 11 a(177) = 7 a(178) = 5 a(179) = 7 a(180) = 5 a(181) = 5 a(182) = 5 a(183) = 6 a(184) = 5 a(185) = 9 a(186) = 5 a(187) = 7 a(188) = 5 a(189) = 9 a(190) = 8 a(191) = 10 a(192) = 5 a(193) = 10 a(194) = 5 a(195) = 11 a(196) = 5 a(197) = 10 a(198) = 5 a(199) = 10 a(200) = 45
On Thu, Dec 15, 2011 at 5:24 PM, Michael Kleber <michael.kleber@gmail.com>wrote:
Ah, yes, good point. That can turn into a computer search in all bases. Nice.
--Michael On Dec 15, 2011 5:09 PM, "Tom Rokicki" <rokicki@gmail.com> wrote:
Only considering the last four digits, for all values of i between 0 and 10000 not divisible by 10, shows 125 at 72 as the highest (next best is 3375 at 56).
This proves that the limit is k=72 at 125, and there is no solution that does not end in "0125" that is not 125 itself.
On Thu, Dec 15, 2011 at 1:43 PM, Michael Kleber <michael.kleber@gmail.com> wrote:
Does someone have a proof for k=72 (in decimal)? Sure seems right, but I don't think we've seen an upper bound on the x that attains the maximum k, which would justify computer-based evidence.
--Michael
On Thu, Dec 15, 2011 at 4:15 PM, N. J. A. Sloane < njas@research.att.com wrote:
> It is 72, I think, for x = 125 Yes, you are right. It seems likely that 72 should suffice for all integers x.
What about the sequence: a(n) = smallest k such that ... ? With a(125) = 72. Could you please submit it? (With keyword "base", of course) Neil
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- -- http://cube20.org/ -- http://golly.sf.net/ --
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- -- http://cube20.org/ -- http://golly.sf.net/ --