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 A210614 Numbers without digit 0 or 5 whose "waterfall sequence" ends in 0,0,0,... 3
 69, 78, 87, 96, 98, 169, 178, 187, 196, 619, 696, 718, 787, 817, 872, 873, 878, 916, 961, 962, 969, 1169, 1178, 1691, 1781, 2987, 6911, 6916, 6961, 6962, 6969, 7817, 7872, 7873, 7878, 8117, 8787, 9116, 9696, 9878 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The "waterfall" sequence S for a given starting value S(1) is defined as S(n)=d(n-1)*d(n) (n>1), where d(n) is the n-th digit of the sequence. When a(0) has a digit 0 or 5, then S is likely to end up in repeating zeros, which is the motivation for the definition of this sequence. LINKS E. Angelini, Waterfalls (of multiplications), Mar 27 2012 E. Angelini, Waterfalls (of multiplications) [Cached copy, with permission] EXAMPLE The waterfall sequence for S(1)=69 is S=(69,54,45,20,16,20,10,0,0,6,12, 0,0,0,0,0,0,6,2,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,2,0,0,0,...) with S(2)=6*9=54, S(3)=9*5=45, S(4)=5*4=20, etc. The last "2" is obtained as 1*2 from the digits of term S(27)=12, thereafter there are no two consecutive nonzero digits and therefore only 0's can follow. Similarly, for S(1)=78, one has S=(78,56,40,30,24,0,0,0,0,8,0,0,0,...), and only zeros thereafter since d(10)=4 is the last nonzero digit having a nonzero neighboring digit (d(9)=2, which yields S(10)=2*4=8). PROG (PARI) is_A210614(n)={!setintersect(["0", "5"], Set(Vec(Str(n)))) & is_A210652(n)} for(n=10, 9999, is_A210614(n) & print1(n", ")) CROSSREFS Sequence in context: A168477 A264045 A295806 * A235226 A015980 A065209 Adjacent sequences:  A210611 A210612 A210613 * A210615 A210616 A210617 KEYWORD nonn,base AUTHOR M. F. Hasler, Mar 27 2012 STATUS approved

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Last modified October 26 04:54 EDT 2021. Contains 348256 sequences. (Running on oeis4.)