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.

A261461 a(n) is the smallest nonzero number that is not a substring of n in its binary representation.

Original entry on oeis.org

1, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 4, 4, 5, 5, 4, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 4, 7, 4, 4, 4, 5, 5, 5, 5, 7, 4, 4, 4, 5, 5, 4, 4, 5, 4, 4, 2, 3, 3, 3, 5, 3, 3, 5, 5, 3, 3, 3, 6, 5, 7, 5, 5, 3, 3, 3, 6, 3, 3
Offset: 0

Views

Author

Reinhard Zumkeller, Aug 30 2015

Keywords

Comments

A261018(n) = a(A260273(n)).
Is a(n) = A091460(n) for n>1? - R. J. Mathar, Sep 02 2015. The lowest counterexample occurs at a(121) = 5 < 6 = A091460(121). - Álvar Ibeas, Sep 08 2020
a(A062289(n))=A261922(A062289(n)); a(A126646(n))!=A261922(A126646(n)). - Reinhard Zumkeller, Sep 17 2015

Links

Crossrefs

Cf. A007088, A030308, A260273, A261018; record values and where they occur: A261466, A261467.
See A261922 for a variant.
Cf. A062289, A144016, A261922, A126646.

Programs

  • Haskell
    import Data.List (isInfixOf)
a261461 x = f $ tail a030308_tabf where
   f (cs:css) = if isInfixOf cs (a030308_row x)
                   then f css else foldr (\d v -> 2 * v + d) 0 cs
  • Mathematica
    fQ[m_, n_] := Block[{g}, g[x_] := ToString@ FromDigits@ IntegerDigits[x, 2]; StringContainsQ[g@ n, g@ m]]; Table[k = 1; While[fQ[k, n] && k < n, k++]; k, {n, 85}] (* Michael De Vlieger, Sep 21 2015 *)
  • Python
    from itertools import count
def a(n):
    b, k = bin(n)[2:], 1
    return next(k for k in count(1) if bin(k)[2:] not in b)
print([a(n) for n in range(86)]) # Michael S. Branicky, Feb 26 2023

Formula

a(n) = A144016(n) + 1 for any n > 0. - Rémy Sigrist, Mar 10 2018

A094461 a[n] is the 5th term in Euclid-Mullin (EM) prime sequence initiated with n-th prime.

Original entry on oeis.org

13, 13, 331, 13, 7, 6163, 7, 571, 13, 10267, 23, 31, 7, 13, 17, 7, 3, 7, 5227, 43, 7, 2371, 7, 61, 19, 3, 7, 13, 3271, 13, 5, 37, 4111, 43, 3, 13, 47, 7, 5011, 360187, 7, 73, 13, 22003, 23, 7, 8863, 5, 7, 6871, 181, 193, 7, 7, 11, 139, 3, 7, 1297, 73, 7, 7, 31, 3, 7
Offset: 1

Views

Author

Labos Elemer, May 06 2004

Keywords

Examples

			First term is p[n], 2nd equals 2;
3rd term is A091460 as largest p-divisor of 2p+1
(occasionally safe primes, A005385);
4th terms listed in A051614; 5th term is here in A094461;
6th, 7th terms in A094462, A094463;

Crossrefs

Cf. A000945, A005385, A051614-A051616, A051308-A051335, A093778-A093782, A094152-A094153, A094460-A094463.

Programs

  • Mathematica
    a[x_]:=First[Flatten [FactorInteger[Apply[Times, Table[a[j], {j, 1, x-1}]]+1]]];ta=Table[0, {168}];a[1]=1; Do[{a[1]=Prime[j], el=5};Print[a[el];ta[[j]]=a[el];j++ ], {j, 1, 168}];ta

A094463 a(n) is the 7th term in Euclid-Mullin (EM) prime sequence initiated with n-th prime.

Original entry on oeis.org

5, 5, 199, 5, 433, 1601, 31, 457, 7109609443, 5, 7, 127, 71, 5, 7, 2620003, 4583, 1217, 5, 67, 6729871, 39334891, 5, 53, 461, 449885311, 1511, 197, 7, 22008559, 19, 1249, 7, 7, 3217, 7, 7, 3931, 7, 110663370509047, 375155719, 29, 28529671, 23, 24603331
Offset: 1

Views

Author

Labos Elemer, May 06 2004

Keywords

Examples

			First term is p(n), 2nd equals 2;
3rd term is A091460 as largest p-divisor of 2p+1
(occasionally safe primes, A005385);
4th terms listed in A051614; 5th term is in A094461;
6th-7th terms in A094462, A094463;

Crossrefs

Cf. A000945, A005385, A051614-A051616, A051308-A051335, A093778-A093782, A094152-A094153, A094460-A094463.

Programs

  • Mathematica
    a[x_]:=First[Flatten [FactorInteger[Apply[Times, Table[a[j], {j, 1, x-1}]]+1]]];ta=Table[0, {168}];a[1]=1; Do[{a[1]=Prime[j], el=6};Print[a[el];ta[[j]]=a[el];j++ ], {j, 1, 168}];ta

A094462 a(n) is the 6th term in Euclid-Mullin (EM) prime sequence initiated with n-th prime.

Original entry on oeis.org

53, 53, 19, 53, 10627, 7, 3571, 271, 84319, 7, 47059, 7, 47, 53, 23971, 11, 13, 5, 7, 201499, 5, 7, 67, 13, 7, 21211, 5, 29, 10696171, 11, 149, 971, 16896211, 11, 58111, 17, 11, 75307, 25105111, 853, 139, 7, 5, 613, 181, 23, 13, 29, 13, 19, 53, 47, 5, 11, 84811
Offset: 1

Views

Author

Labos Elemer, May 06 2004

Keywords

Examples

			First term is p(n), 2nd equals 2;
3rd term is A091460 as largest p-divisor of 2p+1
(occasionally safe primes, A005385);
4th terms listed in A051614; 5th term is in A094461;
6th-7th terms in A094462, A094463;

Crossrefs

Cf. A000945, A005385, A051614-A051616, A051308-A051335, A093778-A093782, A094152-A094153, A094460-A094463.

Programs

  • Mathematica
    a[x_]:=First[Flatten [FactorInteger[Apply[Times, Table[a[j], {j, 1, x-1}]]+1]]];ta=Table[0, {168}];a[1]=1; Do[{a[1]=Prime[j], el=6};Print[a[el];ta[[j]]=a[el];j++ ], {j, 1, 168}];ta

A091461 Smallest number containing in its binary representation substrings forming an arithmetic progression exactly of size n.

Original entry on oeis.org

0, 3, 2, 6, 12, 75, 44, 92, 184, 1208, 1256, 4840, 4792, 36055, 9912, 19832, 39664, 563952, 576464, 4496112, 4499184
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 12 2004

Keywords

Comments

A091460(a(n))=n and A091460(m)<>n for m

Examples

			a(7) = 44->'101100', {0+k*1: 0<=k<7}: bbbbb0 => 1bbbbb => 10bbbb => bb11bb => bbb100 => 101bbb => bb110b.
a(6) > 44: Although there is an arithmetic progression of length 6 in the binary expansion of 44, it is extendable (to length 7).

Extensions

a(12)-a(13) by Álvar Ibeas, Sep 09 2020
a(14)-a(21) by Álvar Ibeas, Sep 12 2020
Showing 1-5 of 5 results.

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