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A061808
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a(n) is the smallest number with all digits odd that is divisible by 2n-1.
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3
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1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 315, 115, 75, 135, 319, 31, 33, 35, 37, 39, 533, 559, 135, 517, 539, 51, 53, 55, 57, 59, 793, 315, 195, 335, 759, 71, 73, 75, 77, 79, 1377, 913, 595, 957, 979, 91, 93, 95, 97, 99, 1111, 515, 315, 535, 1199, 111, 113, 115, 117
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OFFSET
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1,2
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COMMENTS
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Record value for a(n) = (2n-1) * A296009(n).
(1, 3, 5, ..., 19) * 1 = (1, 3, 5, ..., 19)
21 * 15 = 315
29 * 11 = 319
41 * 13 = 533
43 * 13 = 559
61 * 13 = 793
81 * 17 = 1377
127 * 11 = 1397
129 * 15 = 1935
149 * 13 = 1937
167 * 19 = 3173
169 * 33 = 5577
201 * 155 = 31155
299 * 105 = 31395
401 * 133 = 53333
601 * 119 = 71519
633 * 283 = 179139
(the list above is complete)
...
990001 * 12121113 = 11999913991113 (the first A296009(n) > 2n-1).
(End)
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LINKS
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Mathematical Excalibur, Problem 300, Vol. 1 No. 3 p. 3, 2008.
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MAPLE
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Ad[1]:= [1, 3, 5, 7, 9]:
for n from 2 to 9 do Ad[n]:= map(t -> seq(10*t+j, j=[1, 3, 5, 7, 9]), Ad[n-1]) od:
Aod:= [seq(op(Ad[i]), i=1..9)]:
f:= proc(n) local k;
for k from 1 to nops(Aod) do
if Aod[k] mod (2*n-1) = 0 then return(Aod[k]) fi
od;
NotFound
end proc:
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MATHEMATICA
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Table[Block[{k = 2 n - 1}, While[Nand[AllTrue[IntegerDigits@ k, OddQ], Divisible[k, 2 n - 1]], k += 2]; k], {n, 59}] (* Michael De Vlieger, Dec 02 2017 *)
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PROG
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(Magma) a:=[]; for n in [1..120 by 2] do k:=1; while not Set(Intseq(n*k)) subset {1, 3, 5, 7, 9} do k:=k+2; end while; Append(~a, k*n); end for; a; // Marius A. Burtea, Sep 20 2019
(PARI) isoddd(n) = #select(x->((x%2) == 0), digits(n)) == 0;
a(n) = {my(m = 2*n-1, k = 1); while(!isoddd(k*m), k++); k*m; } \\ Michel Marcus, Sep 20 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 30 2001
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STATUS
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approved
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