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 1-6 of 6 results.

A032810 Numbers using only digits 2 and 3.

Original entry on oeis.org

2, 3, 22, 23, 32, 33, 222, 223, 232, 233, 322, 323, 332, 333, 2222, 2223, 2232, 2233, 2322, 2323, 2332, 2333, 3222, 3223, 3232, 3233, 3322, 3323, 3332, 3333, 22222, 22223, 22232, 22233, 22322, 22323, 22332, 22333, 23222, 23223
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Identical to A007931 with substitution of digits 2 -> 3, 1 -> 2, i.e., application of the function A048379 or A256079(n) = n + A002275(A055642(n)). - M. F. Hasler, Mar 21 2015

Links

Crossrefs

Cf. A020458, A143967, A248907 (permutation).
Cf. A032804-A032816 (in other bases), A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032834 (digits 3 & 4), A256290 (digits 4 & 5), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9).

Programs

  • Haskell
    a032810 = f 0 . (+ 1) where
   f y 1 = a004086 y
   f y x = f (10 * y + m + 2) x' where (x', m) = divMod x 2
-- Reinhard Zumkeller, Mar 18 2015
  • Magma
    [n: n in [1..24000] | Set(Intseq(n)) subset {2, 3}]; // Vincenzo Librandi, May 27 2012
  • Magma
    [n eq 1 select 2 else IsOdd(n) select 10*Self(Floor(n/2))+2 else Self(n-1)+1: n in [1..40]]; // Bruno Berselli, May 27 2012
  • Mathematica
    Flatten[Table[FromDigits[#,10]&/@Tuples[{2,3},n],{n,5}]] (* Vincenzo Librandi, May 27 2012 *)
  • PARI
    A032810(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*2 \\ M. F. Hasler, Mar 26 2015
  • Python
    def A032810(n): return int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1<<1)//9 # Chai Wah Wu, Jul 15 2023

Formula

a(n) = f(n+1, 0) with f(n, x) = if n=1 then A004086(x) else f(floor(n/2), 10*x + 2 + n mod 2). - Reinhard Zumkeller, Sep 06 2008
a(n) is Theta(n^(log_2 10)); there are about n^(log_10 2) members of this sequence up to n. - Charles R Greathouse IV, Mar 18 2010
a(n) = A007931(n) + A002275(A000523(n+1)). A055642(a(n)) = A000523(n+1). - M. F. Hasler, Mar 21 2015

A020463 Primes that contain digits 3 and 7 only.

Original entry on oeis.org

3, 7, 37, 73, 337, 373, 733, 773, 3373, 3733, 7333, 33377, 33773, 37337, 77377, 77773, 333337, 333737, 373777, 377737, 733333, 733373, 737773, 773777, 777373, 777737, 3333373, 3333773, 3337333, 3337777, 3377377, 3733333, 3773377, 3773773, 3777377, 7337333, 7337777, 7377373, 7733377, 7737337
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Subsequence of A030096.
Cf. A143967, A020458.

Programs

  • Mathematica
    Flatten[Table[Select[FromDigits/@Tuples[{3,7},n],PrimeQ],{n,7}]] (* Vincenzo Librandi, Jul 27 2012 *)

A284963 Numbers with digits 3 and 8 only.

Original entry on oeis.org

3, 8, 33, 38, 83, 88, 333, 338, 383, 388, 833, 838, 883, 888, 3333, 3338, 3383, 3388, 3833, 3838, 3883, 3888, 8333, 8338, 8383, 8388, 8833, 8838, 8883, 8888, 33333, 33338, 33383, 33388, 33833, 33838, 33883, 33888, 38333, 38338, 38383, 38388, 38833, 38838
Offset: 1

Views

Author

Jaroslav Krizek, Apr 06 2017

Keywords

Crossrefs

Prime terms are in A020464.
Numbers with digits 3 and k only for k = 0 - 2 and 4 - 9: A169966 (k = 0), A032917 (k = 1), A032810 (k = 2), A032834 (k = 4), A284379 (k = 5), A284633 (k = 6), A143967 (k = 7), this sequence (k = 8), A284964 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 8}]
  • Mathematica
    Table[FromDigits/@Tuples[{3,8},n],{n,5}]//Flatten (* Harvey P. Dale, Mar 23 2021 *)

A284964 Numbers with digits 3 and 9 only.

Original entry on oeis.org

3, 9, 33, 39, 93, 99, 333, 339, 393, 399, 933, 939, 993, 999, 3333, 3339, 3393, 3399, 3933, 3939, 3993, 3999, 9333, 9339, 9393, 9399, 9933, 9939, 9993, 9999, 33333, 33339, 33393, 33399, 33933, 33939, 33993, 33999, 39333, 39339, 39393, 39399, 39933, 39939
Offset: 1

Views

Author

Jaroslav Krizek, Apr 06 2017

Keywords

Comments

All terms > 3 are composite.

Crossrefs

Cf. Numbers with digits 3 and k only for k = 0 - 2 and 4 - 9: A169966 (k = 0), A032917 (k = 1), A032810 (k = 2), A032834 (k = 4), A284379 (k = 5), A284633 (k = 6), A143967 (k = 7), A284963 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 9}]
  • Mathematica
    Table[FromDigits/@Tuples[{3,9},n],{n,5}]//Flatten (* Harvey P. Dale, Sep 20 2022 *)

Formula

a(n) = 3 * A032917(n).

A285011 Numbers with digits 7 and 9 only.

Original entry on oeis.org

7, 9, 77, 79, 97, 99, 777, 779, 797, 799, 977, 979, 997, 999, 7777, 7779, 7797, 7799, 7977, 7979, 7997, 7999, 9777, 9779, 9797, 9799, 9977, 9979, 9997, 9999, 77777, 77779, 77797, 77799, 77977, 77979, 77997, 77999, 79777, 79779, 79797, 79799, 79977, 79979
Offset: 1

Views

Author

Jaroslav Krizek, Apr 08 2017

Keywords

Crossrefs

Prime terms are in A020471.
Numbers with digits 7 and k only for k = 0 - 6 and 8 - 9: A204094 (k = 0), A276039 (k = 1), A284921 (k = 2), A143967 (k = 3), A284971 (k = 4), A284380 (k = 5), A256292 (k = 6), A256340 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {7, 9}];
  • Mathematica
    Flatten@ Table[FromDigits /@ Tuples[{7, 9}, n], {n, 5}] (* Giovanni Resta, Apr 10 2017 *)
  • PARI
    a(n,{p=[7,9]})={my(v=binary(n+1));fromdigits(vector(#v-1,i,p[2]*v[i+1]+p[1]*!v[i+1]))} \\ R. J. Cano, Apr 09 2017
  • Python
    def a(n): return int(bin(n+1)[3:].replace('0', '7').replace('1', '9'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jul 09 2021

A343823 Numbers k > 10 such that every permutation of the digits of k is congruent to 3 (mod 4).

Original entry on oeis.org

11, 15, 19, 51, 55, 59, 91, 95, 99, 111, 115, 119, 151, 155, 159, 191, 195, 199, 511, 515, 519, 551, 555, 559, 591, 595, 599, 911, 915, 919, 951, 955, 959, 991, 995, 999, 1111, 1115, 1119, 1151, 1155, 1159, 1191, 1195, 1199, 1511, 1515, 1519, 1551, 1555, 1559
Offset: 11

Views

Author

Ctibor O. Zizka, Apr 30 2021

Keywords

Comments

Also numbers that contain only the digits 1,5,9. More general : Numbers k > 10 such that every permutation of the digits of k is congruent to r (mod m). For m = 4; r = 0 gives A343810, r = 1 gives A143967, r = 2 gives A284632, r = 3 gives this sequence.

Examples

			159 = 4*39 + 3, 195 = 4*48 + 3, 519 = 4*104 + 3, 591 = 4*147 + 3, 915 = 4*228 + 3, 951 = 4*237 + 3.

Crossrefs

Cf. A143967, A284632, A343810.

Programs

  • Mathematica
    Select[Range[11, 1600], AllTrue[Permutations[IntegerDigits[#]], Mod[FromDigits[#1], 4] == 3 &] &] (* Amiram Eldar, Apr 30 2021 *)
Showing 1-6 of 6 results.

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