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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A051810 Numbers with nonzero multiplicative digital root 8.

Original entry on oeis.org

8, 18, 24, 29, 36, 38, 42, 46, 49, 63, 64, 66, 67, 76, 77, 79, 80, 81, 83, 88, 92, 94, 97, 99, 108, 118, 124, 129, 136, 138, 142, 146, 149, 163, 164, 166, 167, 176, 177, 179, 180, 181, 183, 188, 192, 194, 197, 199, 204, 209, 214
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

Links

Crossrefs

Part of histogram of A051802.

Formula

A051802^-1(8)

A051811 Numbers with nonzero multiplicative digital root 9.

Original entry on oeis.org

9, 19, 33, 90, 91, 109, 119, 133, 190, 191, 259, 295, 303, 313, 330, 331, 356, 365, 529, 536, 563, 592, 635, 653, 900, 901, 910, 911, 925, 952, 1009, 1019, 1033, 1090, 1091, 1109, 1119, 1133, 1190, 1191, 1259, 1295, 1303
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

Links

Crossrefs

Part of histogram of A051802.

Programs

  • Mathematica
    nzdr9[n_]:=Module[{idn=Select[IntegerDigits[n],#!=0&]},Times@@idn]; nzdrQ[ n_]:= NestWhile[nzdr9[#]&,n,#>9&]==9; Select[Range[2000],nzdrQ] (* Harvey P. Dale, Sep 09 2014 *)

Formula

A051802^-1(9)

A051813 Number of n-digit numbers with nonzero multiplicative digital root 2.

Original entry on oeis.org

1, 15, 208, 2389, 24845, 243697, 2348885, 22837227, 226507501, 2285904554, 23239957877, 235731610792, 2372897841904, 23686630752065, 235058927877399, 2327977363798607
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051804, A051822.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=2 }

A051822 Number of numbers below 10^n with nonzero multiplicative digital root 2.

Original entry on oeis.org

1, 16, 224, 2613, 27458, 271155, 2620040, 25457267, 251964768, 2537869322, 25777827199, 261509437991, 2634407279895, 26321038031960, 261379965909359, 2589357329707966
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051804, A051813.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=2 }

A086354 Fixed point if (nonzero-digit product)-function at initial value 2^n is iterated.

Original entry on oeis.org

2, 4, 8, 6, 6, 8, 6, 6, 1, 8, 8, 2, 6, 2, 2, 4, 8, 2, 1, 6, 2, 2, 6, 8, 2, 8, 2, 8, 2, 2, 8, 6, 6, 2, 2, 6, 2, 2, 6, 8, 8, 6, 3, 4, 2, 2, 6, 6, 2, 8, 6, 2, 2, 9, 8, 6, 6, 5, 8, 2, 8, 8, 2, 6, 2, 8, 8, 8, 5, 8, 8, 8, 2, 8, 6, 4, 8, 6, 2, 7, 1, 8, 8, 4, 2, 8, 8
Offset: 1

Views

Author

Labos Elemer, Jul 21 2003

Keywords

Examples

			n=20, 2^20=1048576, iteration list={1048576,6720,84,32,6}, so a(20)=6.

Links

Crossrefs

Cf. A051801, A051802, A086353-A086361, A029898, A010888.

Programs

  • Maple
    A051801 := proc(n) local d,j: d:=convert(n,base,10): return mul(`if`(d[j]=0,1,d[j]), j=1..nops(d)): end: A086354 := proc(n) local m: m:=2^n: while(length(m)>1)do m:=A051801(m): od: return m: end: seq(A086354(n),n=1..100); # Nathaniel Johnston, May 04 2011
  • Mathematica
    prd[x_] := Apply[Times, DeleteCases[IntegerDigits[x], 0]] Table[FixedPoint[prd, 2^w], {w, 1, 128}]

Formula

a(n) = A051802(2^n) = fixed point of A051801(2^n).

A051812 Number of n-digit numbers with nonzero multiplicative digital root 1.

Original entry on oeis.org

1, 5, 24, 243, 3048, 35224, 374890, 3766188, 36537927, 348892847, 3315037530, 31399344551, 295789894509, 2769886220702, 25882768895688, 243033400452156
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

Comments

Not counting zero as a one-digit number.

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051803, A051821.

Formula

a(n) = # { i : 10^(n-1) < i < 10^n and A051802(i)=1 }.

A051814 Number of n-digit numbers with nonzero multiplicative digital root 3.

Original entry on oeis.org

1, 7, 40, 240, 1448, 8630, 53545, 371845, 3267453, 36428242, 442762543, 5217693527, 57321559329, 586532407659, 5666269188709, 52728701479194
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051805, A051823.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=3 }

A051815 Number of n-digit numbers with nonzero multiplicative digital root 4.

Original entry on oeis.org

1, 12, 105, 780, 5452, 39979, 336081, 3263355, 34518027, 372779338, 3957184040, 40729856248, 406862880846, 3979167973684, 38556471560342, 374259579575061
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051806, A051824.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=4 }

A051816 Number of n-digit numbers with nonzero multiplicative digital root 5.

Original entry on oeis.org

1, 7, 58, 422, 2872, 19772, 142418, 1096582, 9040811, 78452199, 699839588, 6297456806, 56804155533, 517737762700, 4839960759976, 46837953974511
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051807, A051825.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=5 }

A051817 Number of n-digit numbers with nonzero multiplicative digital root 6.

Original entry on oeis.org

1, 14, 198, 2124, 20894, 208420, 2117454, 21576952, 218613631, 2195038525, 21848423462, 216219614463, 2135812278843, 21121667130245, 209377570378397, 2080106337706143
Offset: 1

Views

Author

Dan Hoey, Dec 09 1999

Keywords

References

  • William Mayne, sci.math, Jun 15 1991

Crossrefs

Cf. A051802, A051808, A051826.

Formula

# { i : 10^(n-1) < i < 10^n and A051802(i)=6 }
Previous Showing 11-20 of 34 results. Next

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