

A210589


Numbers which, when divided by their first digit, have their last digit as remainder.


1



10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 201, 210, 211, 220, 221, 230, 231, 240, 241
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OFFSET

1,1


COMMENTS

Coincides with A071590 up to the 79th term, A071590(79)=310 is not in this sequence.
Charles R Greathouse IV observes that this is an automatic sequence in the terminology of Allouche & Shallit.
See A210582 for the obvious "symmetric" counterpart: first digit = x mod last digit.  M. F. Hasler, Jan 14 2014


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..7000
Charles R Greathouse IV, in reply to E. Angelini, Re: Divided by first digit, have last digit as remainder, SeqFan list, Mar 21 2012
Index entries for 10automatic sequences.


MATHEMATICA

ldrQ[n_]:=Module[{idn=IntegerDigits[n], f, l}, f=First[idn]; l=Last[idn]; Mod[n, f]==l]; Select[Range[10000], ldrQ] (* Harvey P. Dale, Mar 21 2012 *)


PROG

(PARI) is_A210589(x)=x%(x\10^(#Str(x)1))==x%10
(MAGMA) [ n: n in [1..249]  n mod d[#d] eq d[1] where d is Intseq(n) ]; // Bruno Berselli, Mar 23 2012


CROSSREFS

Sequence in context: A267759 A297270 A071590 * A296714 A297147 A325198
Adjacent sequences: A210586 A210587 A210588 * A210590 A210591 A210592


KEYWORD

nonn,base,easy


AUTHOR

Eric Angelini (idea) and M. F. Hasler, Mar 23 2012


STATUS

approved



