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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A256868 Numbers divisible by prime(d+1) for each digit d of their base-8 representation.

Original entry on oeis.org

0, 9, 33, 57, 72, 130, 210, 264, 456, 570, 576, 585, 660, 969, 1040, 1050, 1170, 1365, 1540, 1680, 1995, 2112, 2145, 2508, 2600, 2730, 2860, 2925, 3366, 3648, 3705, 4047, 4104, 4170, 4356, 4488, 4560, 4608, 4620, 4680, 4683, 4809, 4998, 5130, 5250, 5265, 5280, 6825, 7752, 8210, 8320, 8400, 8850, 9240, 9350, 9360, 9555
Offset: 1

Views

Author

M. F. Hasler, Apr 11 2015

Keywords

Comments

The base-8 variant of A256882 - A256884, A256866 - A256870 in bases 2, ..., 10.
A variant of A256878 where digits 0 are forbidden and divisibility by prime(d) is required.

Crossrefs

Cf. A256882, A256883, A256884, A256865 - A256870, A256874 - A256879, A256786.

Programs

  • Mathematica
    Select[Range[0,10000],And@@Divisible[#,Prime[IntegerDigits[#,8]+1]]&] (* Harvey P. Dale, May 06 2015 *)
  • PARI
    is(n,b=8)=!for(i=1,#d=Set(digits(n,b)),n%prime(d[i]+1)&&return)

A256876 Numbers divisible by prime(d) for each digit d in their base-6 representation, none of which may be zero.

Original entry on oeis.org

15, 28, 154, 280, 525, 555, 735, 910, 1036, 1078, 1666, 3795, 4270, 4665, 4690, 5446, 5530, 5572, 5775, 5950, 6202, 7755, 9352, 9982, 10108, 13888, 14014, 15400, 18705, 18885, 18915, 19965, 19995, 20175, 20475, 20625, 21735, 21945, 22605, 26445, 26475, 26565, 26655, 27735, 27995, 28000, 28035
Offset: 1

Views

Author

M. F. Hasler, Apr 11 2015

Keywords

Comments

Base-6 analog of A256786. See A256874 - A256879 for the base-4, ..., base-9 analogs.
See A256866 for a variant where divisibility by prime(d+1) is required instead.
Since digit 0 is not allowed, no terms are divisible by 6, so digits 1 and 2 can't both be present. - Robert Israel, Apr 04 2024

Links

Crossrefs

Cf. A256786, A256874 - A256879, A256868, A256882 - A256884, A256865 - A256870.

Programs

  • Maple
    P:= [2,3,5,7,11]:
filter6:= proc(n) local S,s;
  S:= convert(convert(n,base,6),set);
  if member(0,S) then return false fi;
  n mod mul(P[s],s=S) = 0
end proc:
S1:= {1}; S2:= {2}; S0:= {3,4,5}: R:= select(filter6, S0 union S1 union S2):
for i from 2 to 10 do
  S1:= map(t -> (6*t+1, 6*t+3,6*t+4, 6*t+5), S1) union map(t -> 6*t+1, S0);
  S2:= map(t -> (6*t+2, 6*t+3, 6*t+4, 6*t+5), S2) union map(t -> 6*t+2, S0);
  S0:= map(t -> (6*t+3,6*t+4,6*t+5), S0);
  R:= R union select(filter6, S0) union select(filter6, S1) union select(filter6, S2);
od:
sort(convert(R,list)); # Robert Israel, Apr 04 2024
  • Mathematica
    ndpQ[n_]:=Module[{ds=Union[IntegerDigits[n,6]]},FreeQ[ds,0]&&And@@ Table[ Divisible[n,Prime[i]],{i,ds}]]; Select[Range[20000],ndpQ] (* Harvey P. Dale, May 29 2015 *)
  • PARI
    is(n,b=6)=!for(i=1,#d=Set(digits(n,b)),(!d[i]||n%prime(d[i]))&&return)

Extensions

More terms from Robert Israel, Apr 04 2024

A256878 Numbers divisible by prime(d) for each digit d in their base-8 representation, none of which may be zero.

Original entry on oeis.org

18, 35, 78, 84, 90, 138, 210, 255, 330, 429, 588, 594, 910, 1098, 1170, 1275, 1386, 1530, 1755, 1820, 1950, 2156, 2275, 2706, 3315, 3510, 3927, 3978, 4746, 4758, 4794, 4900, 4914, 5202, 5610, 5850, 6244, 6300, 6412, 6930, 7254, 7410, 7462, 7566, 8778, 8850, 9042, 9354, 9435, 9492
Offset: 1

Views

Author

M. F. Hasler, Apr 11 2015

Keywords

Comments

Base-8 analog of A256786. See A256874 - A256879 for the base-4, ..., base-9 analogs.
See A256868 for a variant where divisibility by prime(d+1) is required instead.

Crossrefs

Cf. A256786, A256874 - A256879, A256868, A256882 - A256884, A256865 - A256870.

Programs

  • PARI
    is(n,b=8)=!for(i=1,#d=Set(digits(n,b)),(!d[i]||n%prime(d[i]))&&return)

A256877 Numbers divisible by prime(d) for each digit d in their base-7 representation, none of which may be zero.

Original entry on oeis.org

8, 10, 114, 120, 195, 264, 286, 400, 408, 450, 456, 500, 650, 744, 750, 780, 792, 1100, 1170, 1200, 1804, 1870, 2802, 2808, 2850, 2886, 3144, 3198, 3600, 4290, 4524, 5202, 5280, 5610, 5655, 5742, 6000, 6798, 7020, 7710, 8010, 8340, 12804, 13200, 14820, 14846, 15210, 19608, 19610
Offset: 1

Views

Author

M. F. Hasler, Apr 11 2015

Keywords

Comments

Base-7 analog of A256786. See A256874 - A256879 for the base-4, ..., base-9 analogs.
See A256867 for a variant where divisibility by prime(d+1) is required instead.

Crossrefs

Cf. A256786, A256874 - A256879, A256867, A256882 - A256884, A256865 - A256870.

Programs

  • PARI
    is(n,b=7)=!for(i=1,#d=Set(digits(n,b)),(!d[i]||n%prime(d[i]))&&return)
Previous Showing 11-14 of 14 results.

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