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 1-5 of 5 results.

A256865 Numbers divisible by prime(d+1) for each digit d of their base-5 representation.

Original entry on oeis.org

0, 6, 10, 30, 50, 60, 110, 126, 150, 156, 168, 180, 210, 231, 250, 260, 300, 310, 378, 550, 630, 660, 726, 750, 756, 780, 810, 840, 900, 930, 1008, 1050, 1250, 1260, 1300, 1310, 1320, 1380, 1410, 1500, 1510, 1530, 1550, 1560, 1680, 1760, 1870, 1890, 1960, 2016, 2268, 2310, 2331, 2618, 2750, 2860, 3124, 3126, 3150, 3156, 3180
Offset: 1

Views

Author

M. F. Hasler, Apr 11 2015

Keywords

Comments

The base-5 variant of A256882 - A256884, A256866 - A256870 in bases 2, ..., 10.
A variant of A256875 where digits 0 are forbidden and divisibility by prime(d) is required.

Examples

			0 is divisible by prime(0+1)=2.
6 = 11_5 and is divisible by prime(1+1)=3.
10 = 20_5 and is divisible by prime(0+1)=2 and by prime(2+1)=5.
n = 1, 2, 3, 4 are not divisible by prime(n+1) = 3, 5, 7, 11. 5=10_5 is not divisible by prime(0+1)=2; 7=12_5 is not divisible by prime(2+1)=5, etc.

Crossrefs

Cf. A256882, A256883, A256884, A256866-A256870, A256874-A256879, A256786.

Programs

  • PARI
    is(n,b=5)=!for(i=1,#d=Set(digits(n,b)),n%prime(d[i]+1)&&return)

A256870 Numbers divisible by prime(d+1) for each digit d of their base-10 representation.

Original entry on oeis.org

0, 20, 44, 111, 120, 171, 200, 210, 220, 290, 440, 520, 1020, 1110, 1113, 1200, 1710, 1914, 2000, 2010, 2020, 2030, 2100, 2145, 2200, 2220, 2310, 2420, 2900, 3220, 3381, 4004, 4048, 4400, 4444, 5200, 5525, 6120, 7220, 8280, 9338
Offset: 1

Views

Author

M. F. Hasler, Apr 11 2015

Keywords

Comments

A variant of A256786 where digits 0 are forbidden and divisibility by prime(d) is required.
See A256882 - A256884, A256866 - A256869 for the analog in bases 2, ..., 9.

Examples

			0 is divisible by prime(0+1)=2.
n = 1,...,9 are not divisible by prime(n+1) = 3, 5, ..., 29, respectively.
20 is divisible by prime(2+1)=5 and by prime(0+1)=2. The same is true for any other 2...20...0 =  2*10^k*(10^m-1)/9; k >= 1, m >= 0.
44 is divisible by prime(4+1)=11.

Crossrefs

Cf. A256882, A256883, A256884, A256865 - A256869, A256874 - A256879, A256786.

Programs

  • PARI
    is(n,b=10)=!for(i=1,#d=Set(digits(n,b)),n%prime(d[i]+1)&&return)

A256869 Numbers divisible by prime(d+1) for each digit d of their base-9 representation.

Original entry on oeis.org

0, 20, 84, 90, 180, 252, 273, 455, 510, 738, 756, 810, 816, 840, 900, 1224, 1275, 1460, 1470, 1620, 1640, 2090, 2185, 2268, 2450, 2541, 3080, 3289, 3553, 4199, 4590, 5434, 6570, 6642, 6660, 6804, 7290, 7326, 7344, 7380, 7395, 7470, 7560, 7866, 8100, 8160, 8190, 8778, 8841, 8925, 9282
Offset: 1

Views

Author

M. F. Hasler, Apr 11 2015

Keywords

Comments

The base-9 variant of A256882 - A256884, A256866 - A256870 in bases 2, ..., 10.
A variant of A256879 where digits 0 are forbidden and divisibility by prime(d) is required.
From Robert Israel, Aug 01 2019: (Start)
If n is in the sequence and is even, then 9*n is in the sequence.
If n is in the sequence and 9^k > n, then (9^k+1)*n is in the sequence.
All multiples of 223092870 are in the sequence.
(End)

Links

Crossrefs

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

Programs

  • Maple
    P:= [seq(ithprime(i),i=1..9)]:
filter:= proc(n) local L;
  L:= convert(convert(n,base,9),set);
  L:= map(t -> P[t+1],L);
  n mod convert(L,`*`) = 0
end proc:
select(filter, [$0..10000]); # Robert Israel, Aug 01 2019
  • PARI
    is(n,b=9)=!for(i=1,#d=Set(digits(n,b)),n%prime(d[i]+1)&&return)

Formula

a(n) ~ 223092870*n. - Robert Israel, Aug 01 2019

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
Showing 1-5 of 5 results.

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