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 A069570 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. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS FORMULA a(n) % 10 = (n-1) % 9 + 1. - M. F. Hasler, Sep 27 2016 EXAMPLE 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. MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A069571. Sequence in context: A055572 A052040 A328781 * A279367 A020731 A229300 Adjacent sequences:  A069567 A069568 A069569 * A069571 A069572 A069573 KEYWORD nonn,base AUTHOR Amarnath Murthy, Mar 24 2002 EXTENSIONS Corrected (inserted missing terms) and extended by Jeremy Gardiner, Jun 17 2010 Definition clarified by M. F. Hasler, Sep 27 2016 STATUS approved

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Last modified May 14 04:27 EDT 2021. Contains 343872 sequences. (Running on oeis4.)