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 A038770 Numbers divisible by at least one of their digits. 12
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 30, 31, 32, 33, 35, 36, 39, 40, 41, 42, 44, 45, 48, 50, 51, 52, 55, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 75, 77, 80, 81, 82, 84, 85, 88, 90, 91, 92, 93, 95, 96, 99, 100, 101, 102 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A038769(a(n)) > 0; complement of A038772. The decimal digit strings of this sequence are a regular language, since it is the union of A011531 and A121022 .. A121029 which are likewise regular languages. Some computer state machine manipulation for this union shows a minimum deterministic finite automaton (DFA) matching the digit strings of this sequence has 11561 states. Reversing strings (so least significant digit first) reduces to 1699 states, or reverse and allow high 0's (which become trailing 0's due to the reverse) reduces to 1424 states. The latter are tractable sizes for the linear recurrence in A327560. - Kevin Ryde, Dec 04 2019 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Index entries for 10-automatic sequences FORMULA a(n) ~ n. - Charles R Greathouse IV, Jul 22 2011 EXAMPLE 35 is included because 5 is a divisor of 35, but 37 is not included because neither 3 nor 7 is a divisor of 37. MATHEMATICA Select[Range[110], MemberQ[Divisible[#, Cases[IntegerDigits[#], Except[0]]], True]&] (* Harvey P. Dale, Jun 20 2011 *) PROG (Haskell) a038770 n = a038770_list !! (n-1) a038770_list = filter f [1..] where f u = g u where g v = v > 0 && (((d == 0 || r > 0) && g v') || r == 0) where (v', d) = divMod v 10; r = mod u d -- Reinhard Zumkeller, Jul 30 2015, Jun 19 2011 (PARI) is(n)=my(v=vecsort(eval(Vec(Str(n))), , 8)); for(i=if(v[1], 1, 2), #v, if(n%v[i]==0, return(1))); 0 \\ Charles R Greathouse IV, Jul 22 2011 (Python) def ok(n): return any(n%int(d) == 0 for d in str(n) if d != '0') print(list(filter(ok, range(1, 103)))) # Michael S. Branicky, May 20 2021 CROSSREFS Cf. A327560 (counts), A038772 (complement), A034709, A034837, A038769. Sequence in context: A359415 A080682 A182049 * A342591 A193176 A263314 Adjacent sequences: A038767 A038768 A038769 * A038771 A038772 A038773 KEYWORD base,easy,nonn,nice AUTHOR Henry Bottomley, May 04 2000 STATUS approved

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Last modified September 22 10:30 EDT 2023. Contains 365520 sequences. (Running on oeis4.)