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.

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A062942 Numbers k that, when expressed in base 6 and then interpreted in base 10, give a multiple of k.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 308, 4920, 11284, 11914, 144393, 195453, 518659, 866358, 925148, 1010765, 1172718, 1369865, 2141968, 2557924, 4287428, 4296908, 6064590, 8219190, 15347544, 16891738, 18409156, 18532263, 21880744, 23693054, 25724568, 25781448, 88115915, 93066844
Offset: 1

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Author

Erich Friedman, Jul 21 2001

Keywords

Comments

Zero followed by A032546. [From R. J. Mathar, Oct 02 2008]

Examples

			308 in base 6 is 1232, which interpreted in base 10 is 1232 = 4*308.

Crossrefs

Cf. A062845, A062846, A062847, A062848, A062849, A062850, A062853, A062864, A062865, A062884, A062889, A062891, A062920, A062921, A062922, A062923, A062925, A062928, A062929, A062930, A062931, A062934, A062937, A062939, A062943, A062944.

Extensions

More terms from Naohiro Nomoto, Aug 06 2001
Offset changed to 1 and a(29)-a(34) from Georg Fischer, Mar 13 2023

A062885 Smallest multiple of n with property that digits are even and each digit is two less (mod 10) than the previous digit, if such a multiple exists; otherwise -1.

Original entry on oeis.org

0, 2, 2, 6, 4, 20, 6, 42, 8, 864, 20, 42086, 420, 208, 42, 420, 64, 8642086, 864, 642086, 20, 42, 42086, 6420864, 864, -1, 208, 864, 420, 8642, 420, 86420864208642, 64, 420864208642086, 8642086, 420, 864, 86420864208642, 642086, 86420864208642086420864208642, -1, 642086420864208642, 42, 86, 2086420864, 6420864208642086420, 6420864, 2086420864208642086, 864, 208642, -1, 864208642086420864208642086420864
Offset: 0

Views

Author

Amarnath Murthy, Jun 28 2001

Keywords

Examples

			a(7) = 42 = 7*6 has decreasing even digits.
For n = 25, the conditions require that the desired multiple 25k have k even, i.e., 25k = 25(2i) = 50i = (5i)(10). Thus the final digit is 0, so the next-to-last digit must be 2, but this is impossible since 5i always ends in 0 or 5. Thus a(25) = -1. - _John W. Layman_, Nov 01 2001

Links

Crossrefs

Cf. A062884.

Extensions

More terms and better description from John W. Layman, Nov 01 2001
Further terms from Jud McCranie, Nov 01 2001

A062886 Smallest multiple of 2n+1 with property that digits are odd and each digit is two more (mod 10) than the previous digit; or 0 if no such number exists.

Original entry on oeis.org

1, 3, 5, 7, 9, 913, 13, 135, 357, 57, 357, 1357, 0, 135, 9135, 91357, 9135791357913, 35, 13579, 13579135791, 7913, 3579135791357913, 135, 913579135791, 79135, 357, 1357913, 7913579135, 57, 1357, 7913579135791357913579, 9135, 791357913579135791357913579135
Offset: 0

Views

Author

Amarnath Murthy, Jun 28 2001

Keywords

Comments

The size of terms of this sequence varies wildly. For example, a(453) has 755 digits, while a(456)=913. The only numbers n for which a(n)=0 up to n=500 are those for which 2*n+1 is divisible by 25. - Nathaniel Johnston, May 19 2011

Examples

			a(7) = 135 = 3*(2*7 + 1) has increasing odd digits.
a(12) does not exist because a number in base 10 divisible by 25 ends with 00, 25, 50 or 75, so a(12)=0.

Links

Crossrefs

Cf. A062884, A062885.

Programs

  • Maple
    A062886 := proc(n) local d,j,k,p,val: p:=2*n+1: if(p mod 25 = 0)then return 0: fi: for j from 1 do for d from 1 to 9 by 2 do val:=0: for k from 1 to j do val:=val+10^(j-k)*((d+2*(k-1)) mod 10): od: if(val mod p = 0)then return val: fi: od: od: end: seq(A062886(n),n=0..30); # Nathaniel Johnston, May 19 2011
  • Mathematica
    a[n_] := Module[{d, j, k, p, val}, p = 2*n+1; If[p ~Mod~ 25 == 0, Return[0]]; For[j = 1, True, j++, For[d = 1, d <= 9, d += 2, val = 0; For[k = 1, k <= j, k++, val = val + 10^(j-k)*((d + 2*(k-1)) ~Mod~ 10)]; If[val ~Mod~ p == 0, Return[val]]]]];
Table[a[n], {n, 0, 34}] (* Jean-François Alcover, Apr 17 2025, after Nathaniel Johnston *)

Extensions

More terms from Sascha Kurz, Mar 23 2002
a(6) and example corrected by, and terms after a(15) from Nathaniel Johnston, May 19 2011

A062887 Smallest multiple of 2n+1 with the property that its digits are odd and each digit is two less (mod 10) than the previous digit, or 0 if no such number exists.

Original entry on oeis.org

1, 3, 5, 7, 9, 319, 975, 75, 7531, 19, 197531975319, 3197, 75, 5319, 319, 31, 3197531975319, 53197531975, 1975319, 975, 531975, 1975319753197, 19753197531975, 75319753197531, 319753197531975319, 753197531975319753
Offset: 0

Views

Author

Amarnath Murthy, Jun 28 2001

Keywords

Comments

Conjecture: The only numbers n for which a(n)=0 are those for which 2*n+1 is divisible by 125. - Sean A. Irvine, Apr 14 2023

Examples

			a(7) = 975 = 13*75 has decreasing odd digits.

Crossrefs

Cf. A062884, A062885.

Programs

  • Maple
    l := 0:for i from 1 to 35 do for j from 1 to 5 do a := 0:for h from 1 to i do a := 10*a+((2*j+1-2*h) mod 10):end do:l := l+1:q[l] := a:end do:end do:s := seq(q[ll],ll=1..l); for i from 1 to 65 do k := 1:while((s[k] mod (2*i-1))>0) do k := k+1:end do: w[i] := s[k]:end do:seq(w[j],j=1..65);

Extensions

More terms from Sascha Kurz, Mar 25 2002
Previous Showing 11-14 of 14 results.

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