A109783
a(n) is the largest possible K such that there exists a K-digit in base n integer M such that for each N=1,2,...,K, the integer given by the first N digits of M in base n is divisible by N.
Original entry on oeis.org
2, 6, 7, 10, 11, 18, 17, 22, 25, 26, 28, 35, 39, 38, 39, 45, 48, 48, 52, 53, 56, 58, 61, 65, 67, 69, 73, 75, 79, 83, 83
Offset: 2
Alec Mihailovs (alec(AT)mihailovs.com), Aug 13 2005
a(10)=25 because for 25-digit number 3608528850368400786036725, 3 is divisible by 1, 36 is divisible by 2, 360 is divisible by 3, ..., 3608528850368400786036725 is divisible by 25 and there is no 26-digit number with similar properties.
A271374
Total number of polydivisible numbers in base n.
Original entry on oeis.org
3, 16, 38, 128, 324, 1068, 2569, 8381, 20457, 58174, 148059, 441493, 916146, 3722968, 8407790, 23909586, 64576509, 178009925, 466027279, 1409607602, 3507905894, 9694292108, 25391646456, 73838562312, 191793924162, 550333004128
Offset: 2
There are a(10) = 20457 polydivisible numbers in base 10, which are listed in A144688.
A132185
a(n) is the largest number beginning with 1 such that, for any m, the number formed from the first m digits of a(n) is congruent to n mod m.
Original entry on oeis.org
144408645048225636603816, 1725676121534561296189, 188276429246387492222, 19838179232721317143537, 12764828245698443284086, 176903816597810123057, 18626438463030625206604, 19352559475935751347112, 16128296082816884008108
Offset: 0
Philippe LALLOUET (philip.lallouet(AT)orange.fr), Nov 04 2007
a(3) = 19838179232721317143537 because 19 == 3 mod 2, 198 == 3 mod 3, 1983 == 3 mod 4,..., 19838179232721317143537 == 3 mod 23; but no additional digit makes a 3 mod 24 number.
A324205
The largest zeroless polydivisible number in base n (written in base 10).
Original entry on oeis.org
1, 8, 57, 616, 7465, 117636, 2054451, 42912896, 987654564, 25915636800, 736867916290, 23297940244152, 789024560946557, 29174313555611252, 1147797409031506920, 48649494479090875520, 2178349008754768757872, 104127216885225393371514
Offset: 2
a(3) = (22)_3 = 8.
a(4) = (321)_4 = 57.
a(5) = (4431)_5 = 616.
a(6) = (54321)_6 = 7465.
a(7) = (666651)_7 = 117636.
a(8) = (7654463)_8 = 2054451.
a(9) = (88665375)_9 = 42912896.
a(10) = 987654564.
a(11) = (AA99779559)_11 = 25915636800.
a(12) = (BA9876A836A)_12 = 736867916290.
A380359
a(n) is the number of integers in base n such that all the integers given by their first k digits are divisible by k and which cannot be extended further.
Original entry on oeis.org
1, 3, 8, 21, 54, 145, 367, 1039, 2492, 6709, 16799, 46610, 95597, 368134, 831886, 2245056, 6084180, 15798495, 41456343, 119786906, 292818176, 788255058, 2061079489, 5753392327, 14984432350
Offset: 2
a(10)=2492 because from all A271374(10)=20457 polydivisible numbers, only 2492 cannot be further expanded into a larger polydivisible number. One such number is 4836545640368400: 4 is divisible by 1, 48 is divisible by 2, 483 is divisible by 3, 4836 is divisible by 4, and so on until 4836545640368400 which is divisible by 16; but one cannot extend it further since no digit (0 to 9) appended to 4836545640368400 would result in a number divisible by k=17.
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