A075115 -id:A075115 - cp's OEIS frontend

A075014 Smallest k such that the concatenation k, k-1 is divisible by n; or 0 if no such number exists.

1, 1, 2, 3, 1, 5, 2, 3, 5, 1, 17, 17, 6, 9, 11, 3, 16, 5, 7, 21, 2, 17, 18, 29, 26, 17, 5, 33, 8, 11, 35, 3, 17, 33, 26, 41, 11, 7, 17, 21, 13, 47, 4, 17, 41, 41, 27, 29, 9, 51, 50, 17, 21, 5, 61, 61, 35, 27, 52, 41, 29, 35, 68, 45, 6

Offset: 1

Amarnath Murthy, Sep 01 2002

			a(14) = 9 as 14 divides 98.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A075114, A075115, A075116, A075117.

skc[n_]:=Module[{k=1},While[Mod[FromDigits[Flatten[IntegerDigits/@{k,k-1}]],n] != 0,k++];k]; Array[skc,70] (* Harvey P. Dale, Mar 04 2023 *)

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

A075016 Smallest k such that the concatenation k, k-1,k-2 is divisible by n; or 0 if no such number exists.

Original entry on oeis.org

2, 2, 2, 4, 2, 2, 2, 4, 4, 2, 12, 4, 105, 2, 2, 4, 7, 4, 18, 22, 2, 12, 11, 4, 27, 118, 4, 106, 21, 2, 23, 14, 12, 34, 2, 4, 112, 18, 105, 22, 15, 2, 39, 34, 7, 14, 9, 4, 141, 52, 7, 118, 58, 4, 12, 106, 18, 50, 38, 22, 10, 54, 106, 14, 157

Offset: 1

Amarnath Murthy, Sep 01 2002

			a(11) = 12 as 11 divides 121110.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A075113, A075114, A075115, A075117.

skc[n_]:=Module[{k=2},While[Mod[FromDigits[Flatten[IntegerDigits/@ Range[ k,k-2,-1]]],n]!=0,k++];k]; Array[skc,70] (* Harvey P. Dale, Nov 01 2019 *)

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

A075013 Smallest k such that the decimal concatenation of k and k+1 is divisible by n.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 5, 5, 4, 9, 16, 1, 7, 5, 4, 19, 3, 13, 22, 19, 16, 27, 2, 19, 24, 7, 31, 5, 31, 19, 27, 19, 16, 3, 9, 31, 26, 41, 7, 19, 28, 37, 20, 27, 4, 51, 20, 19, 16, 49, 52, 35, 32, 31, 49, 5, 22, 31, 66, 19, 32, 27, 58, 19, 9, 49, 6, 35, 28, 9, 26, 67, 13, 63, 49, 79, 16

Offset: 1

Amarnath Murthy, Sep 01 2002

			a(16) = 19 as 16 divides 1920.

Cf. A075114, A075115, A075116, A075117.

With[{cnct=Table[FromDigits[Flatten[IntegerDigits/@{n,n+1}]],{n,100}]},Table[ Position[cnct,?(Divisible[#,k]&),1,1],{k,100}]]//Flatten (* _Harvey P. Dale, Apr 11 2020 *)

for(n=1,100,k=1:while((k*(10^floor(log(k+1)/log(10)+1))+k+1)%n>0,k=k+1):print1(k","))

Corrected and extended by Ralf Stephan, Mar 23 2003

A075017 Smallest k such that the concatenation k, k+1,k+2,k+3 is divisible by n; or 0 if no such number exists.

Original entry on oeis.org

1, 1, 3, 3, 2, 3, 2, 3, 3, 7, 8, 3, 7, 17, 12, 3, 5, 3, 19, 17, 24, 15, 17, 3, 22, 7, 3, 17, 17, 27, 6, 3, 15, 5, 2, 3, 9, 19, 15, 17, 15, 45, 44, 37, 12, 17, 39, 3, 45, 47, 21, 41, 52, 3, 37, 17, 57, 17, 62, 57, 53, 53, 66, 3, 7, 15, 2, 21, 63, 17, 12, 3, 6, 9, 72

Offset: 1

Amarnath Murthy, Sep 01 2002

			a(7) = 2 as 7 divides 2345.

Cf. A075113, A075114, A075115, A075116.

isok(k, n) = my(v = Str(k)); for (j=1, 3, v = concat(v, Str(k+j))); (eval(v) % n) == 0;
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Jan 21 2017

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

A075018 Smallest k such that the concatenation k, k-1,k-2,k-3 is divisible by n; or 0 if no such number exists.

Original entry on oeis.org

3, 3, 3, 5, 3, 3, 5, 5, 6, 3, 18, 9, 11, 5, 3, 15, 13, 15, 19, 23, 18, 29, 29, 15, 28, 11, 33, 5, 4, 3, 40, 15, 18, 13, 18, 15, 28, 19, 24, 23, 26, 39, 7, 51, 33, 29, 55, 15, 53, 53, 30, 63, 54, 33, 18, 5, 57, 41, 56, 63, 69, 71, 60, 15, 63

Offset: 1

Amarnath Murthy, Sep 01 2002

			a(7) = 5 as 7 divides 5432.

Cf. A075113, A075114, A075115, A075116, A075117.

Transpose[Flatten[Table[Select[Reverse[Partition[Range[100,0,-1], 4,1]], Divisible[FromDigits[ Flatten[IntegerDigits/@#]],n]&,1],{n,70}],1]] [[1]] (* Harvey P. Dale, Nov 22 2011 *)

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

cp's OEIS Frontend

A075014 Smallest k such that the concatenation k, k-1 is divisible by n; or 0 if no such number exists.

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A075016 Smallest k such that the concatenation k, k-1,k-2 is divisible by n; or 0 if no such number exists.

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A075013 Smallest k such that the decimal concatenation of k and k+1 is divisible by n.

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A075017 Smallest k such that the concatenation k, k+1,k+2,k+3 is divisible by n; or 0 if no such number exists.

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A075018 Smallest k such that the concatenation k, k-1,k-2,k-3 is divisible by n; or 0 if no such number exists.

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Extensions