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 A235164 Numbers whose digits, when the number is written in base n+1, are a permutation of 1...n, and such that for all k in {1,...,n} the first k digits (still in base n+1) form a number divisible by k. 1
 1, 27, 57, 2285, 7465, 874615, 1391089, 1538257, 381654729, 559922224824157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See sequence A163574 (which lists, for each n, the smallest term with n digits) for further discussion, in particular the proof that n must be odd, and that there is no further term with less than 13 digits.  See sequence A235133 for the version where the terms (up to 9 digits) are written down in base 10. LINKS EXAMPLE The terms with 5 digits in base 6 are 2285 = 14325[6] and 7465 = 54321[6], since these numbers are divisible by 5, and 14[6] = 10, 143[6] = 63, 1432[6] = 380 are divisible by 2, 3 and 4, respectively, and the same is the case for 54[6] = 34, 543[6] = 207 and 5432[6] = 1244. PROG (PARI) for(n=1, 9, p=vector(n, i, (n+1)^(i-1)); for(k=0, n!-1, d=numtoperm(n, k); for(j=2, n, sum(i=1, j, d[i]*p[j-i+1])%j &&next(2)); print1(d*vector(n, i, (n+1)^(n-i))~", "))) (Python) def vgen(n, b): ....if n == 1: ........t = list(range(1, b)) ........for i in range(1, b): ............u = list(t) ............u.remove(i) ............yield i, u ....else: ........for d, v in vgen(n-1, b): ............for g in v: ................k = d*b+g ................if not k % n: ....................u = list(v) ....................u.remove(g) ....................yield k, u A235164_list = [a for n in range(2, 15, 2) for a, b in vgen(n-1, n)] # Chai Wah Wu, Jun 07 2015 CROSSREFS Sequence in context: A080864 A260440 A039459 * A157500 A180574 A107580 Adjacent sequences:  A235161 A235162 A235163 * A235165 A235166 A235167 KEYWORD nonn,base,more AUTHOR M. F. Hasler, Jan 04 2014 EXTENSIONS a(10) from Chai Wah Wu, Jun 07 2015 STATUS approved

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Last modified May 6 02:09 EDT 2021. Contains 343579 sequences. (Running on oeis4.)