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Search: id:A116436
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| A116436 |
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Numbers n which when sandwiched between two 1's give a multiple of n. |
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+0
10
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| 1, 11, 13, 77, 91, 137, 9091, 909091, 5882353, 10989011, 12987013, 52631579, 76923077, 90909091, 4347826087, 9090909091, 13698630137, 909090909091, 3448275862069, 10989010989011, 12987012987013, 76923076923077
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All k-digit numbers that divide 10^{k+1} + 1. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 23 2008
Notice the infinite pattern n=(90..90..90)91 with 1n1/n=21, e.g. 1911/91=190911/9091=19090911/909091=21. - Zak Seidov (zakseidov(AT)yahoo.com), Apr 22 2008
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LINKS
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Franklin T. Adams-Watters, Table of n, a(n) for n = 1..87
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EXAMPLE
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77 is a member since 1771 is a multiple of 77 (77*23).
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MATHEMATICA
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f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[1, 14] (*Chandler*)
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PROGRAM
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(PARI program from Franklin T. Adams-Watters, Apr 22 2008) A116436(k) = {local(l, d, lb, ub); d=divisors(10^(k+1)+1); l=[]; lb=10^(k-1); ub=10*lb; for(i=1, #d, if(d[i]>=lb&&d[i]<ub, l=concat(l, [d[i]]))); l}
l=[]; for(i=1, 60, l=concat(l, A116436(i))); l
(PARI) A116436k(k) = { local(l, d, lb, ub); d=divisors(10^(k+1)+1); l=[]; lb=10^(k-1); ub=10*lb; for(i=1, #d, if(d[i]>=lb&&d[i]<ub, l=concat(l, [d[i]]))); l} l=[]; for(i=1, 16, l=concat(l, A116436k(i))); l - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 23 2008
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CROSSREFS
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Cf. A116437-A116444.
Cf. A136296.
Sequence in context: A057189 A105290 A072580 this_sequence A056446 A023317 A056436
Adjacent sequences: A116433 A116434 A116435 this_sequence A116437 A116438 A116439
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KEYWORD
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base,nonn
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AUTHOR
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Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 15 2006
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