cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A073910 Smallest number m such that m and the product of digits of m are both divisible by 3n, or 0 if no such number exists.

Original entry on oeis.org

3, 6, 9, 168, 135, 36, 273, 168, 999, 0, 0, 1296, 0, 378, 495, 384, 0, 1296, 0, 0, 1197, 0, 0, 1368, 3525, 0, 2997, 672, 0, 0, 0, 384, 0, 0, 735, 1296, 0, 0, 0, 0, 0, 3276, 0, 0, 3915, 0, 0, 3168, 7497, 0, 0, 0, 0, 5994, 0, 7896, 0, 0, 0, 0, 0, 0, 7938, 2688, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Amarnath Murthy, Aug 18 2002

Keywords

Comments

Here 0 is regarded as not divisible by any number.
a(n) = 0 if 10 divides 3n or n contains a prime divisor > 9. - Sascha Kurz, Aug 23 2002

Links

Crossrefs

Cf. A073906, A073908, A073909, A073911, A073912, A085124.

Programs

  • Maple
    f := 3:for i from 1 to 1000 do b := ifactors(f*i)[2]: if b[nops(b)][1]>9 or (f*i mod 10) =0 then a[i] := 0:else j := 0:while true do j := j+f*i:c := convert(j,base,10):d := product(c[k],k=1..nops(c)): if (d mod f*i)=0 and d>0 then a[i] := j:break:fi:od:fi:od:seq(a[k],k=1..1000);

Formula

a(n) = A085124(3*n). - R. J. Mathar, Jun 21 2018

Extensions

More terms from Sascha Kurz, Aug 23 2002

A073908 Smallest number m such that m and the product of digits of m are both divisible by 7n, or 0 if no such number exists.

Original entry on oeis.org

7, 378, 273, 476, 175, 378, 3577, 728, 1197, 0, 0, 672, 0, 7742, 735, 784, 0, 3276, 0, 0, 7497, 0, 0, 7896, 1575, 0, 7938, 69776, 0, 0, 0, 12768, 0, 0, 37975, 3276, 0, 0, 0, 0, 0, 71736, 0, 0, 9765, 0, 0, 8736, 47677, 0, 0, 0, 0, 7938, 0, 74872, 0, 0, 0, 0, 0, 0, 7497
Offset: 1

Views

Author

Amarnath Murthy, Aug 18 2002

Keywords

Comments

Here 0 is regarded as not divisible by any number.
a(n) = 0 if n is divisible by 10 or contains a prime divisor > 9. - Sascha Kurz, Aug 23 2002

Examples

			a(8) = 728 is divisible by 7*8 = 56 and also 7*2*8 = 112 = 2*56.

Crossrefs

Cf. A073906, A085124, A073909, A073910, A073911, A073912.

Programs

  • Maple
    f := 7:for i from 1 to 400 do b := ifactors(f*i)[2]: if b[nops(b)][1]>9 or (f*i mod 10) =0 then a[i] := 0:else j := 0:while true do j := j+f*i:c := convert(j,base,10): d := product(c[k],k=1..nops(c)): if (d mod f*i)=0 and d>0 then a[i] := j:break:fi: od:fi:od:seq(a[k],k=1..400);

Formula

a(n) = A085124(7*n). - R. J. Mathar, Jun 21 2018

Extensions

More terms from Sascha Kurz, Aug 23 2002

A073911 Smallest number m such that m and the product of digits of m are both divisible by 5n, or 0 if no such number exists.

Original entry on oeis.org

5, 0, 135, 0, 525, 0, 175, 0, 495, 0, 0, 0, 0, 0, 3525, 0, 0, 0, 0, 0, 735, 0, 0, 0, 55125, 0, 3915, 0, 0, 0, 0, 0, 0, 0, 1575, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15975, 0, 0, 0, 37975, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 155625, 0, 0, 0, 0, 0, 31995, 0, 0
Offset: 1

Views

Author

Amarnath Murthy, Aug 18 2002

Keywords

Comments

Here 0 is regarded as not divisible by any number.
a(n) = 0 if n is divisible by 2 or contains a prime divisor > 9. - Sascha Kurz, Aug 23 2002

Crossrefs

Cf. A073906, A085124, A073908, A073909, A073910, A073912.

Programs

  • Maple
    f := 5:for i from 1 to 400 do b := ifactors(f*i)[2]: if b[nops(b)][1]>9 or (f*i mod 10) =0 then a[i] := 0:else j := 0:while true do j := j+f*i:c := convert(j,base,10): d := product(c[k],k=1..nops(c)): if (d mod f*i)=0 and d>0 then a[i] := j:break:fi: od:fi:od:seq(a[k],k=1..400);

Formula

a(n) = A085124(5*n). - R. J. Mathar, Jun 21 2018

Extensions

More terms from Sascha Kurz, Aug 23 2002

A073912 Smallest number m such that m and the product of digits of m are both divisible by 8n, or 0 if no such number exists.

Original entry on oeis.org

8, 48, 168, 288, 0, 384, 728, 448, 1368, 0, 0, 384, 0, 784, 0, 2688, 0, 3168, 0, 0, 7896, 0, 0, 2688, 0, 0, 4968, 12768, 0, 0, 0, 4864, 0, 0, 0, 4896, 0, 0, 0, 0, 0, 8736, 0, 0, 0, 0, 0, 2688, 74872, 0, 0, 0, 0, 22896, 0, 14784, 0, 0, 0, 0, 0, 0, 33768, 14848, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Amarnath Murthy, Aug 18 2002

Keywords

Comments

Here 0 is regarded as not divisible by any number.
a(n) = 0 if 5 divides n or n contains a prime divisor > 9. - Sascha Kurz, Aug 23 2002 [Corrected by Sean A. Irvine, Dec 23 2024]

Crossrefs

Cf. A073906, A085124, A073908, A073909, A073910, A073911.

Programs

  • Maple
    f := 8:for i from 1 to 400 do b := ifactors(f*i)[2]: if b[nops(b)][1]>9 or (f*i mod 10) =0 then a[i] := 0:else j := 0:while true do j := j+f*i:c := convert(j,base,10): d := product(c[k],k=1..nops(c)): if (d mod f*i)=0 and d>0 then a[i] := j:break:fi: od:fi:od:seq(a[k],k=1..400);

Formula

a(n) = A085124(8*n). - R. J. Mathar, Jun 21 2018

Extensions

More terms from Sascha Kurz, Aug 23 2002
Showing 1-4 of 4 results.

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