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 1-3 of 3 results.

A254338 Initial digits of A254143 in decimal representation.

Original entry on oeis.org

1, 4, 7, 1, 2, 3, 3, 4, 6, 1, 1, 2, 2, 2, 3, 3, 3, 4, 6, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2
Offset: 1

Views

Author

Reinhard Zumkeller, Feb 27 2015

Keywords

Comments

a(n) = A000030(A254143(n));
also initial digits of A254323: a(n) = A000030(A254323(n)).
all terms are of the form u*v mod 10, where u <= v and belonging to {1,3,4,6,7}, the distinct elements of A254397:
length of k-th run of consecutive 1s = A005993(k-2), k > 1;
length of k-th run of consecutive 2s = k*(k+1)/2 = A000217(k), k >= 1;
length of k-th run of consecutive 3s = k+1, k >= 1;
length of k-th run of consecutive 4s = A065033(k-1);
n with a(n) = 4: A237424(n) = (10^a+10^b+1)/3 with b = 0, see also A093137, A133384;
n with a(n) = 6: A237424(n) = (10^a+10^b+1)/3 with a = b; A005994(a(n)) = 6 for n > 1; see also A199682;

Links

Crossrefs

Cf. A254143, A254323, A000030, A254339, A005993, A000217, A065033.

Programs

  • Haskell
    a254338 = a000030 . a254143
  • PARI
    listA237424(lim)=my(v=List(),a,t); while(1, for(b=0,a, t=(10^a+10^b+1)/3; if(t>lim, return(Set(v))); listput(v, t)); a++)
do(lim)=my(v=List(),u=listA237424(lim),t); for(i=1,#u, for(j=1,i, t=u[i]*u[j]; if(t>lim,break); listput(v,t))); apply(n->digits(n)[1], Set(v)) \\ Charles R Greathouse IV, May 13 2015

A254143 Products of any two not necessarily distinct terms of A237424.

Original entry on oeis.org

1, 4, 7, 16, 28, 34, 37, 49, 67, 136, 148, 238, 259, 268, 334, 337, 367, 469, 667, 1156, 1258, 1336, 1348, 1369, 1468, 2278, 2338, 2359, 2479, 2569, 2668, 3334, 3337, 3367, 3667, 4489, 4669, 6667, 11356, 11458, 12358, 12469, 12478, 13336, 13348, 13468, 13579
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 28 2015

Keywords

Comments

Digits are in nondecreasing order for all terms in decimal representation;
a(396) = 1123456789 = 3367 * 333667 is the smallest term containing all nonzero decimal digits: A254323(396) = 123456789;
A254323(n) = A137564(a(n)).

Examples

			Initial terms of A237424: 1, 4, 7, 34, 37, 67, 334, 337, 367, 667, 3334 ...
.  n | a(n) = A237424(i) * A237424(j)
. ---+-------------------------------
.  1 |    1 = 1 * 1   = A237424(1)^2
.  2 |    4 = 1 * 4   = A237424(1) * A237424(2)
.  3 |    7 = 1 * 7   = A237424(1) * A237424(3)
.  4 |   16 = 4 * 4   = A237424(2)^2
.  5 |   28 = 4 * 7   = A237424(2) * A237424(3)
.  6 |   34 = 1 * 34  = A237424(1) * A237424(4)
.  7 |   37 = 4 * 37  = A237424(1) * A237424(5)
.  8 |   49 = 7 * 7   = A237424(3)^2
.  9 |   67 = 1 * 67  = A237424(1) * A237424(6)
. 10 |  136 = 4 * 34  = A237424(2) * A237424(4)
. 11 |  148 = 4 * 37  = A237424(2) * A237424(5)
. 12 |  238 = 7 * 34  = A237424(3) * A237424(4)
. 13 |  259 = 7 * 37  = A237424(3) * A237424(5)
. 14 |  268 = 4 * 67  = A237424(2) * A237424(6)
. 15 |  334 = 1 * 334 = A237424(1) * A237424(7)
. 16 |  337 = 1 * 337 = A237424(1) * A237424(8)
. 17 |  367 = 1 * 367 = A237424(1) * A237424(9)
. 18 |  469 = 7 * 67  = A237424(3) * A237424(6)
. 19 |  667 = 1 * 34  = A237424(1) * A237424(10)
. 20 | 1156 = 34 * 34 = A237424(4)^2
see link for more.

Links

Crossrefs

Subsequence of A009994.
Cf. A237424, A254323, A137564, A254338 (initial digits), A254339 (final digits).

Programs

  • Haskell
    import Data.Set (empty, fromList, deleteFindMin, union)
import qualified Data.Set as Set (null)
a254143 n = a254143_list !! (n-1)
a254143_list = f a237424_list [] empty where
   f xs'@(x:xs) zs s
     | Set.null s || x < y = f xs zs' (union s $ fromList $ map (* x) zs')
     | otherwise           = y : f xs' zs s'
     where zs' = x : zs
           (y, s') = deleteFindMin s
  • PARI
    listA237424(lim)=my(v=List(),a,t); while(1, for(b=0,a, t=(10^a+10^b+1)/3; if(t>lim, return(Set(v))); listput(v, t)); a++)
list(lim)=my(v=List(),u=listA237424(lim),t); for(i=1,#u, for(j=1,i, t=u[i]*u[j]; if(t>lim,break); listput(v,t))); Set(v) \\ Charles R Greathouse IV, May 13 2015

A254339 Final digits of A254143 in decimal representation.

Original entry on oeis.org

1, 4, 7, 6, 8, 4, 7, 9, 7, 6, 8, 8, 9, 8, 4, 7, 7, 9, 7, 6, 8, 6, 8, 9, 8, 8, 8, 9, 9, 9, 8, 4, 7, 7, 7, 9, 9, 7, 6, 8, 8, 9, 8, 6, 8, 8, 9, 8, 8, 9, 8, 8, 9, 9, 9, 9, 9, 8, 4, 7, 7, 7, 7, 9, 9, 7, 6, 8, 6, 8, 9, 8, 8, 8, 9, 9, 9, 8, 6, 8, 8, 8, 9, 9, 8, 8
Offset: 1

Views

Author

Reinhard Zumkeller, Feb 23 2015

Keywords

Comments

a(n) = A254143(n) mod 10;
also final digits of A254323: a(n) = A254323(n) mod 10.

Links

Crossrefs

Cf. A254143, A254323, A010879, A254398, A254338.

Programs

  • Haskell
    a254339 = flip mod 10 . a254143
  • PARI
    listA237424(lim)=my(v=List(),a,t); while(1, for(b=0,a, t=(10^a+10^b+1)/3; if(t>lim, return(Set(v))); listput(v, t)); a++)
do(lim)=my(v=List(),u=listA237424(lim),t); for(i=1,#u, for(j=1,i, t=u[i]*u[j]; if(t>lim,break); listput(v,t))); apply(n->n%10, Set(v)) \\ Charles R Greathouse IV, May 13 2015
Showing 1-3 of 3 results.

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