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A069570
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Numbers n in which the k-th digit (counted from the right) is nonzero and either a divisor or a multiple of k, for all 1 <= k <= number of digits of n.
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6
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1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 41, 42, 43, 44, 45, 46, 47, 48, 49, 61, 62, 63, 64, 65, 66, 67, 68, 69, 81, 82, 83, 84, 85, 86, 87, 88, 89, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125
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OFFSET
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1,2
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COMMENTS
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The units digits are 1, ..., 9 repeating (period 9). From n = 10 on, the 10's digits are { 1, 2, 4, 6, 8 } each repeated 9 times, and then starting over with 1. Similarly, starting with the first 3-digit term, the 100's digits are {1, 3, 6, 9}, each repeated 45 times, then starting over with 1. From the first 4-digit term on, the 1000's digits are { 1, 2, 4, 8 }, each repeated 180 times, then starting over with 1, etc. - M. F. Hasler, Sep 27 2016
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LINKS
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FORMULA
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EXAMPLE
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The only restriction on the units digit is that it is nonzero. Therefore all single-digit numbers are included.
23 is a term because the 1st digit from the right is 3 which is a multiple of 1, and the 2nd digit from the right is 2 which is a multiple and also divisor of 2.
More generally, the second digit from the right ("10s digit") must be 1 or even.
Similarly, the third digit from the right must be 1, 3 6 or 9.
As all repunits are in the sequence, the sequence is infinite.
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MATHEMATICA
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Select[Range@ 125, Times @@ Map[Boole, MapIndexed[If[#1 == 0, False, Total@ Boole@ {First@ Divisible[#2, #1], First@ Divisible[#1, #2]} > 0] &, Reverse@ IntegerDigits@ #]] > 0 &] (* Michael De Vlieger, Sep 27 2016 *)
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PROG
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(PARI) select( is(n)=!for(i=1, #n=Vecrev(digits(n)), (!n[i]||(n[i]%i&&i%n[i]))&&return), [1..125]) \\ M. F. Hasler, Sep 27 2016
(PARI) is(n) = {my(d = digits(n)); for(i=1, #d, m=min(d[#d+1-i], i); if(m==0, return(0)); if((d[#d+1-i] + i)%m!=0, return(0))); 1} \\ David A. Corneth, Sep 27 2016
(PARI) A069570(n, s, k, d)={until(!n\=#d, s+=10^(k++-1)*(d=select(d->!(k%d&&d%k), [1..9]))[n--%#d+1]); s} \\ M. F. Hasler, Sep 28 2016
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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Corrected (inserted missing terms) and extended by Jeremy Gardiner, Jun 17 2010
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STATUS
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approved
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