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 1-4 of 4 results.

A262377 Primes in A262358.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 31, 43, 47, 61, 67, 71, 17, 19, 79, 89, 23, 83, 101, 107, 103, 109, 113, 97, 29, 37, 41, 53, 127, 137, 157, 167, 251, 257, 269, 281, 419, 359, 431, 353, 439, 59, 73, 163, 313, 331, 373, 659, 709, 761, 701, 857, 877, 883, 941, 971, 977
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 20 2015

Keywords

Comments

a(n) = A262358(A262378(n));
a permutation of the prime numbers, cf. A262363.

Links

Crossrefs

Cf. A262358, A010051, A262378, A262363.

Programs

  • Haskell
    a262377 n = a262377_list !! (n-1)
a262377_list = filter ((== 1) . a010051') $ map a262358 [1..]

A262360 Fixed points of A262356 and of A262358.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 42, 4410, 3060996
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 19 2015

Keywords

Comments

A261466(a(n)) = a(n).

Links

Crossrefs

Cf. A262356, A262358.

Programs

  • Haskell
    a262360 n = a262360_list !! (n-1)
a262360_list = [x | x <- [1..], a262356 x == x]

Extensions

a(15) from Alois P. Heinz, Sep 20 2015

A262378 Positions of prime numbers in A262358.

Original entry on oeis.org

2, 3, 5, 7, 11, 20, 23, 26, 27, 34, 37, 39, 40, 50, 54, 55, 70, 74, 76, 77, 86, 87, 88, 95, 100, 103, 104, 107, 113, 115, 119, 122, 127, 129, 133, 137, 147, 153, 154, 171, 192, 200, 201, 211, 215, 216, 218, 227, 229, 238, 253, 258, 266, 267, 269, 286, 287
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 20 2015

Keywords

Comments

A262377(n) = A262358(a(n)).

Links

Crossrefs

Cf. A262358, A010051, A262377.

Programs

  • Haskell
    a262378 n = a262378_list !! (n-1)
a262378_list = filter ((== 1) . a010051' . a262358) [1..]

A262356 a(1) = 1; for n > 1, let s denote the digit-string of a(n-1) with the first digit omitted. Then a(n) is the smallest number not yet present which starts with s, omitting leading zeros.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 13, 30, 14, 40, 15, 50, 16, 60, 17, 70, 18, 80, 19, 90, 21, 100, 22, 23, 31, 101, 102, 24, 41, 103, 32, 25, 51, 104, 42, 26, 61, 105, 52, 27, 71, 106, 62, 28, 81, 107, 72, 29, 91, 108, 82, 200, 33, 34, 43, 35, 53
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 19 2015

Keywords

Comments

A simplified variation of A262282.
A permutation of the positive integers with inverse A262358;
A262363 and A262371 give the primes and where they occur: A262363(n)=a(A262371(n)).
a(A262393(n)) = A262390(n).
It seems clear that every number will appear, but it would be nice to have a formal proof. - N. J. A. Sloane, Sep 20 2015

Links

Crossrefs

Cf. A262283, A262282, A262358 (inverse), A262360 (fixed points), A262374 (binary counterpart), A262363 (primes), A262371, A000030, A262390 (starting with 1), A262393.

Programs

  • Haskell
    import Data.List (isPrefixOf, delete, genericIndex)
import Data.Set (singleton, notMember, insert)
a262356 n = a262356_list !! (n-1)
a262356_list = 1 : f "" (singleton "1") where
   f xs s = (read ys :: Int) : f (dropWhile (== '0') ys') (insert ys s)
     where ys@(_:ys') = head
             [vs | vs <- zss, isPrefixOf xs vs, notMember vs s]
   zss = map show [2..]
  • Mathematica
    a[1] = 1; a[n_] := a[n] = Module[{s, k}, s = Rest[IntegerDigits[a[n - 1]]] //. {(0).., d__} :> {d}; For[k = 2, True, k++, If[FreeQ[Array[a, n - 1], k], If[s == {0}, Return[k], If[IntegerDigits[k][[1 ;; Length[s]]] == s, Return[k]]]]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 12 2019 *)
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.