The OEIS is supported by the many generous donors to the OEIS Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A329300 a(n) is (apparently) the largest number whose digits are in nondecreasing order in bases n and n+1. 6
 1, 26, 343, 9374, 3203, 411942, 1203135, 12555566, 23577999, 475857425, 78497711, 1840723325, 44509735045, 11166989789, 9181683711, 1240214273284785, 93417582527, 538955006315, 81324126339, 123196100516, 3851792910943, 5652942368056, 4967531840023463 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS In the Data section, each value for n < 9 has been confirmed as the largest such number < 10^10000, and each of the remaining values has been confirmed as the largest such number < 10^1000. LINKS Table of n, a(n) for n=2..24. EXAMPLE The only numbers whose digits are in nondecreasing order in base 2 are the numbers of the form 2^k-1 (k >= 0); of those, the only numbers whose digits are in nondecreasing order in base 3 are 0 = 0_2 = 0_3 and 1 = 1_2 = 1_3. The larger of these numbers is 1, so a(2) = 1. Up to at least 10^10000, the only numbers whose digits are in nondecreasing order in both base 3 and base 4 are 0 = 0_3 = 0_4, 1 = 1_3 = 1_4, 2 = 2_3 = 2_4, 5 = 12_3 = 11_4, and 26 = 222_3 = 122_4. The largest of these numbers is 26, so a(3) = 26. A329294 lists the numbers (up to at least 10^10000) whose digits are in nondecreasing order in both base 4 and base 5, the largest of which is 343, so a(4) = 343. The following table lists the values of a(n) for n = 2..24 with their base-n and base-(n+1) expansions (where the letters a, b, c, etc. represent the digit values 10, 11, 12, etc., respectively): . n | a(n) in base 10 | a(n) in base n | a(n) in base n+1 ---+------------------+------------------+----------------- 2 | 1 | 1_2 | 1_3 3 | 26 | 222_3 | 122_4 4 | 343 | 11113_4 | 2333_5 5 | 9374 | 244444_5 | 111222_6 6 | 3203 | 22455_6 | 12224_7 7 | 411942 | 3333666_7 | 1444446_8 8 | 1203135 | 4455677_8 | 2233346_9 9 | 12555566 | 25555888_9 | 12555566_10 10 | 23577999 | 23577999_10 | 12344555_11 11 | 475857425 | 2246777aa_11 | 113444555_12 12 | 78497711 | 22356abb_12 | 13355666_13 13 | 1840723325 | 23447abcc_13 | 136677777_14 14 | 44509735045 | 22234ccccd_14 | 125789999a_15 15 | 11166989789 | 455577aae_15 | 2999abddd_16 16 | 9181683711 | 223455fff_16 | 1566aadee_17 17 | 1240214273284785 | 223333444588g_17 | 115669aaaffff_18 18 | 93417582527 | 88aaabhhh_18 | 599cdeefg_19 19 | 538955006315 | 1cdhhhiiii_19 | 111138ffff_20 20 | 81324126339 | 33adfffgj_20 | 23347ffff_21 21 | 123196100516 | 3588ghjkk_21 | 258cfffgg_22 22 | 3851792910943 | 34449ijlll_22 | 234677888c_23 23 | 5652942368056 | 33466ikmmm_23 | 238ceefffg_24 24 | 4967531840023463 | 3688bdfkkmmn_24 | 22255aaabcdd_25 CROSSREFS Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), A329296 (b=6), A329297 (b=7), A329298 (b=8), A329299 (b=9). Sequence in context: A035708 A252826 A042306 * A053494 A054938 A161526 Adjacent sequences: A329297 A329298 A329299 * A329301 A329302 A329303 KEYWORD nonn,base AUTHOR Jon E. Schoenfield, Nov 17 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 19:10 EST 2023. Contains 367540 sequences. (Running on oeis4.)