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 1-7 of 7 results.

A063432 Triangle read by rows in which k-th entry in row n is representation of n in base k, for 1 <= k <= n.

Original entry on oeis.org

1, 11, 10, 111, 11, 10, 1111, 100, 11, 10, 11111, 101, 12, 11, 10, 111111, 110, 20, 12, 11, 10, 1111111, 111, 21, 13, 12, 11, 10, 11111111, 1000, 22, 20, 13, 12, 11, 10, 111111111, 1001, 100, 21, 14, 13, 12, 11, 10, 1111111111, 1010, 101, 22, 20, 14, 13
Offset: 1

Views

Author

Henry Bottomley, Jul 20 2001

Keywords

Comments

Representation of n in base 1 is defined to be a concatenation of n 1's.
It is difficult to write twenty-one in base 11 using decimal digits.
Representation in bases greater than 10 are written in base 10. This is really nasty! - N. J. A. Sloane, Dec 06 2002

Examples

			Rows start (1), (11, 10), (111, 11, 10), (1111, 100, 11, 10), etc.

Crossrefs

Cf. A063431.
Rows are effectively the reverse of A001731, A001732, A001733, A001734, A001735, A001736, A008707, A008708, A008709, A008710, A008711, A008712, A008713, A008714, A008715, A008716, A008717, etc.
Columns are truncated versions of A000042, A007088, A007089, A007090, A007091, A007092, A007093, A007094, A007095, A000027 and perhaps A055649, etc.
Without the 1st column becomes A004053.

Programs

  • Mathematica
    f[n_] := Flatten[ Append[ {FromDigits[ Table[1, {n}]] }, Table[ FromDigits[ IntegerDigits[n, i]], {i, 2, n}]]]; Flatten[ Table[ f[n], {n, 1, 10}]] (* Robert G. Wilson v *)

A072803 a(n) is n written in base n mod 10, or 0 if n mod 10 = 0.

Original entry on oeis.org

1, 10, 10, 10, 10, 10, 10, 10, 10, 0, 11111111111, 1100, 111, 32, 30, 24, 23, 22, 21, 0, 111111111111111111111, 10110, 212, 120, 100, 42, 36, 34, 32, 0, 1111111111111111111111111111111, 100000, 1020, 202, 120, 100, 52, 46, 43, 0
Offset: 1

Views

Author

Labos Elemer, Jul 12 2002

Keywords

Examples

			In base 1, n =11...11=n written n times; in base 0 baseform is taken as 0.

Crossrefs

Cf. A008713, A072804-A072807.

Programs

  • Mathematica
    Table[BaseForm[w, Mod[w, 10]], {w, 1, 128}]

A072805 Primes of form 4k+3 written in base 3.

Original entry on oeis.org

10, 21, 102, 201, 212, 1011, 1121, 1202, 2012, 2111, 2122, 2221, 10002, 10211, 10222, 11201, 11212, 12011, 12121, 20001, 20012, 20122, 21002, 21101, 21211, 22021, 22102, 22212, 100022, 100202, 101001, 101111, 102101, 102112, 110021
Offset: 1

Views

Author

Labos Elemer, Jul 12 2002

Keywords

Examples

			83 ~ 10002 in base 3.

Crossrefs

Cf. A008713, A072803-A072807.

Programs

  • Mathematica
    Do[s=Prime[n]; If[Mod[s, 4]==3, Print[BaseForm[s, 3]]], {n, 1, 256}]

A072807 n-th prime prime(n) written in base (prime(n) (mod prime(n-1))).

Original entry on oeis.org

111, 101, 111, 23, 1101, 101, 10011, 113, 45, 11111, 101, 221, 101011, 233, 125, 135, 111101, 151, 1013, 1001001, 211, 1103, 225, 141, 1211, 1100111, 1223, 1101101, 1301, 91, 2003, 345, 10001011, 149, 10010111, 421, 431, 2213, 445, 455, 10110101
Offset: 2

Views

Author

Labos Elemer, Jul 12 2002

Keywords

Examples

			Eventually non-decimal digit symbols appear, as in case of 307=17d, in base 14 = 307 mod 293.

Links

Crossrefs

Cf. A008713, A072803, A072804, A072805, A072806.

Programs

  • Maple
    a:= proc(n) local b, p, l;
      p:= ithprime(n); b:= irem(p, prevprime(p));
      if b=1 then l:= 1$p
    else l:= ""; while p>0 do l:= irem(p, b, 'p'), l od
      fi; parse(cat(l))
    end:
seq(a(n), n=2..62);  # Alois P. Heinz, Sep 05 2019
  • Mathematica
    Table[BaseForm[Prime[w], Mod[Prime[w], Prime[w-1]]], {w, 2, 128}]
Join[{111},FromDigits[IntegerDigits[#[[2]],Mod[#[[2]],#[[1]]]]]&/@ Partition[ Prime[Range[2,50]],2,1]] (* Harvey P. Dale, Jul 03 2021 *)
  • PARI
    a(n) = {my(p=prime(n), q=prime(n-1)); if ((p % q) != 1, d=digits(p, p % q); if (#select(x->(x>9), d), 0, fromdigits(d, 10)), fromdigits(vector(p, k, 1), 10));} \\ Michel Marcus, Sep 05 2019

Extensions

Name corrected by Michel Marcus, Sep 05 2019

A072804 n-th prime prime(n) written in base (prime(n) (mod 4)).

Original entry on oeis.org

10, 10, 11111, 21, 102, 1111111111111, 11111111111111111, 201, 212, 11111111111111111111111111111, 1011, 1111111111111111111111111111111111111, 11111111111111111111111111111111111111111, 1121, 1202, 11111111111111111111111111111111111111111111111111111, 2012
Offset: 1

Views

Author

Labos Elemer, Jul 12 2002

Keywords

Examples

			4k+1 primes are written in base 1, while 4k+3 primes are in base 3.

Links

Crossrefs

Cf. A008713, A072803, A072805, A072806, A072807.

Programs

  • Mathematica
    Table[FromDigits@ If[#2 == 1, ConstantArray[1, #1], IntegerDigits[#1, #2]] & @@ {#, Mod[#, 4]} &@ Prime@ w, {w, 17}] (* Michael De Vlieger, Sep 04 2019 *)
  • PARI
    a(n) = {my(p=prime(n)); if ((p % 4) != 1, fromdigits(digits(p, p % 4), 10), fromdigits(vector(p, k, 1), 10));} \\ Michel Marcus, Sep 04 2019

A072806 Primes of the form 6k+5 written in base 5.

Original entry on oeis.org

10, 21, 32, 43, 104, 131, 142, 203, 214, 241, 313, 324, 401, 412, 423, 1011, 1022, 1044, 1132, 1143, 1204, 1231, 1242, 1402, 1413, 1424, 2001, 2012, 2023, 2034, 2111, 2133, 2221, 2232, 2342, 2403, 2414, 3013, 3024, 3101, 3134, 3211, 3233, 3244, 3321
Offset: 1

Views

Author

Labos Elemer, Jul 12 2002

Keywords

Examples

			41 = 25 + 3*5 + 1 = 131_5.

Links

Crossrefs

Cf. A007091, A007528.
Cf. A008713, A072803, A072804, A072805, A072807.

Programs

  • Mathematica
    Do[s=Prime[n]; If[Mod[s, 6]==5, Print[BaseForm[s, 5]]], {n, 1, 256}]
FromDigits[IntegerDigits[#, 5]] & /@  Select[Table[6 n + 5, {n, 0, 100}], PrimeQ] (* Harvey P. Dale, Oct 05 2023 *)
  • PARI
    lista(nn) = for (n=0, nn, if (isprime(p=6*n+5), print1(fromdigits(digits(p, 5)), ", "))); \\ Michel Marcus, Jul 09 2018

Formula

a(n) = A007091(A007528(n)). - Michel Marcus, Jul 09 2018

A063431 Square array read by antidiagonals of n written in base k (n,k>0).

Original entry on oeis.org

1, 1, 11, 1, 10, 111, 1, 2, 11, 1111, 1, 2, 10, 100, 11111, 1, 2, 3, 11, 101, 111111, 1, 2, 3, 10, 12, 110, 1111111, 1, 2, 3, 4, 11, 20, 111, 11111111, 1, 2, 3, 4, 10, 12, 21, 1000, 111111111, 1, 2, 3, 4, 5, 11, 13, 22, 1001, 1111111111, 1, 2, 3, 4, 5, 10, 12, 20, 100
Offset: 1

Views

Author

Henry Bottomley, Jul 20 2001

Keywords

Comments

It is difficult to write ten in base 11 using decimal digits.

Examples

			Rows start (1, 1, 1, 1, 1,...), (11, 10, 2, 2, 2,...), (111, 11, 10, 3, 3,...), (1111, 100, 11, 10, 4,...), etc.

Crossrefs

Cf. A063432. Rows start effectively as the reverse of A001731, A001732, A001733, A001734, A001735, A001736, A008707, A008708, A008709, A008710, A008711, A008712, A008713, A008714, A008715, A008716, A008717 etc. Columns are A000042, A007088, A007089, A007090, A007091, A007092, A007093, A007094, A007095, A000027 and perhaps A055649 etc.
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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