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A235133 Numbers whose (decimal) digits are a permutation of 1...n for some n, such that for all k in {1,...,n} the first k digits form a number divisible by k, when considered as representation in base n+1. 1
1, 123, 321, 14325, 54321, 3254167, 5234761, 5674321, 381654729 (list; graph; refs; listen; history; text; internal format)



See sequence A163574 for further discussion, in particular the proof that n must be odd, and that there is no further term with less than 13 digits.  There are several options for representing the terms with 13 and more digits, e.g., continuing to write the number d[1]*10^(n-1)+...+d[n]*10^0, or concatenation of the "digits", written in base 10, even when they are larger than 9.

See sequence A235164 for the value of the terms when the n digits are read in base n+1, as it is also done in A163574.


Table of n, a(n) for n=1..9.


a(n) = concatenation of digits of x = A235164(n) when written in base b = A055642(x)+1 = (# digits of x)+1.


a(2) = 123 is in the sequence, because in base 4, 12[4]=6 is divisible by 2 and 123[4] = 27 = A235164(2) is divisible by 3. The same is the case for 321, where 32[4]=14 is even and 321[4] = 57 = A235164(3) is divisible by 3.

For the 9-digit term 381654729, the initial digits are to be interpreted in base 10: 38, 318, ..., 381654729 are divisible by 2, 3, ..., 9, respectively.


(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, 10^(n-i))~", ")))


Sequence in context: A004965 A216382 A269751 * A179612 A091331 A248556

Adjacent sequences:  A235130 A235131 A235132 * A235134 A235135 A235136




M. F. Hasler, Jan 03 2014



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Last modified July 21 22:02 EDT 2019. Contains 325210 sequences. (Running on oeis4.)