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 1-10 of 10 results.

A050682 Positions of 5's in A048288.

Original entry on oeis.org

9, 20, 22, 24, 28, 33, 40, 46, 56, 61, 72, 87
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Links

Crossrefs

Cf. A000422, A046464, A048288, A050679, A050680, A050681.

Extensions

a(11)-a(12) from Sean A. Irvine, Aug 17 2021
Offset changed to 1 by Jinyuan Wang, Sep 04 2021

A050679 Positions of 2's in A048288.

Original entry on oeis.org

2, 3, 4, 6, 7, 11
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Links

Crossrefs

Cf. A000422, A046461, A048288, A050680, A050681, A050682.

Programs

  • Mathematica
    Select[Range[2,12],PrimeOmega[FromDigits[Flatten[IntegerDigits[Range[#,1,-1]]]]]==2 &] (* Jayanta Basu, May 30 2013 *)

Extensions

Offset changed to 1 by Jinyuan Wang, Sep 04 2021

A050680 Positions of 3's in A048288.

Original entry on oeis.org

5, 10, 12, 13, 31, 38, 43, 49, 51, 55, 59, 60, 76, 83, 85, 97, 117, 118
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Links

Crossrefs

Cf. A000422, A046462, A048288, A050679, A050681, A050682.

Extensions

a(13)-a(16) from Sean A. Irvine, Aug 17 2021
Offset changed to 1 by and a(17)-a(18) from Jinyuan Wang, Sep 04 2021

A050681 Positions of 4's in A048288.

Original entry on oeis.org

8, 14, 16, 19, 21, 23, 37, 57, 67, 70, 79, 88, 106
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Links

Crossrefs

Cf. A000422, A046463, A048288, A050679, A050680, A050682.

Extensions

a(9)-a(13) from Sean A. Irvine, Aug 17 2021
Offset changed to 1 by Jinyuan Wang, Sep 04 2021

A050678 Index of first occurrence of n in A048288.

Original entry on oeis.org

82, 2, 5, 8, 9, 15, 17, 30, 26, 18, 91, 53
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Links

Crossrefs

Cf. A000422, A050676, A048288.

Programs

  • Mathematica
    Join[{1},Table[i=1; While[PrimeOmega[FromDigits[Flatten[IntegerDigits[Range[i,1,-1]]]]]!=n,i++]; i,{n,2,10}]] (* Jayanta Basu, May 30 2013 *)

Extensions

a(11)-a(12) from Sean A. Irvine, Aug 17 2021
Edited by N. J. A. Sloane, Sep 04 2021

A050677 Erroneous duplicate of A048288.

Original entry on oeis.org

1, 2, 2, 2, 3, 2, 2, 4, 5, 3, 2, 3, 3, 4, 6, 4, 7, 10, 4, 5, 4, 5, 4, 5, 6, 9, 9, 5, 7, 8, 3, 6, 5, 7, 9, 8, 4, 3, 6, 5, 8, 6, 3, 8, 7, 5, 7, 7, 3, 6, 3, 7, 12, 14, 3, 5, 4, 6, 3, 3, 5, 9, 6, 6, 7, 7, 4, 8, 8, 4, 9, 5, 7, 8, 10, 3, 7, 6, 4, 9, 10, 1, 3, 8, 3
Offset: 1

Views

Author

Keywords

A046460 Number of prime factors of concatenation of numbers from 1 up to n, with multiplicity.

Original entry on oeis.org

0, 3, 2, 2, 3, 8, 2, 5, 4, 3, 6, 6, 3, 3, 3, 4, 5, 6, 6, 10, 8, 6, 4, 6, 5, 9, 8, 7, 4, 7, 3, 6, 6, 2, 8, 9, 4, 4, 6, 9, 5, 7, 4, 7, 10, 7, 5, 8, 6, 10, 3, 9, 8, 14, 5, 5, 6, 4, 4, 8, 3, 8, 5, 10, 6, 8, 3, 10, 7, 6, 6, 7, 3, 9, 6, 6, 5, 6, 6, 10, 6, 7, 6, 7, 6
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1998

Keywords

Links

Crossrefs

Cf. A007908, A046461, A046462, A046463, A046464, A046465, A046466, A046467, A046468, A048288.

Programs

  • Mathematica
    Join[{1},Table[PrimeOmega[FromDigits[Flatten[IntegerDigits[Range[i]]]]],{i,2,35}]] (* Jayanta Basu, Jun 02 2013 *)
  • PARI
    conc(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); \\ A007908
a(n) = bigomega(conc(n)); \\ Michel Marcus, Oct 16 2019

Extensions

Offset 1 and a(1)=0 from Michel Marcus, Oct 16 2019
More terms from Sean A. Irvine, Apr 10 2021

A050687 Numbers k such that A000422(k) is squarefree.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 16, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 49, 50, 51, 52, 55, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Links

Crossrefs

Cf. A000422, A048288, A048342, A050675, A050688.

Extensions

More terms from and name clarified by Sean A. Irvine, Aug 17 2021
Offset changed to 1 by Jinyuan Wang, Sep 04 2021

A050688 Numbers k such that A000422(k) is nonsquarefree.

Original entry on oeis.org

8, 9, 15, 17, 18, 26, 27, 35, 36, 44, 45, 53, 54, 56, 62, 63, 71, 72, 80, 81, 89, 90, 98, 99, 107, 108, 109
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			a(2)=9 because 987654321 = 3^2 * 17^2 * 379721.

Links

Crossrefs

Cf. A013929, A000422, A048288, A048342, A050687, A050675.

Extensions

Definition corrected by Charles R Greathouse IV, Sep 20 2012
a(17)-a(24) and name corrected by Sean A. Irvine, Aug 17 2021
a(25)-a(27) from Daniel Suteu, Aug 18 2021

A351741 Numbers k such that the concatenation of 1,2,...,k and the concatenation of k,k-1,...,1 have the same number of prime factors, counted with multiplicity.

Original entry on oeis.org

1, 3, 4, 5, 7, 10, 13, 16, 23, 26, 31, 32, 37, 39, 51, 54, 56
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, Feb 17 2022

Keywords

Comments

Numbers k such that A001222(A007908(k)) = A001222(A000422(k)).

Examples

			a(3) = 4 is a term because 1234 = 2*617 and 4321 = 29*149 each have two prime factors.

Crossrefs

Cf. A000422, A001222, A007908, A048288.

Programs

  • Maple
    dcat:= (a,b) -> a*10(1+ilog10(b))+b:
a:= 1: b:= 1: R:= 1:
for n from 2 to 40 do
a:= dcat(n,a);
b:= dcat(b,n);
if numtheory:-bigomega(a) = numtheory:-bigomega(b) then R:= R,n fi
od:
R;
  • Mathematica
    Select[Range[32], SameQ @@ PrimeOmega@{FromDigits@ Flatten@ #, FromDigits@ Flatten@ Reverse[#]} &@ IntegerDigits@ Range[#] &] (* Michael De Vlieger, Feb 17 2022 *)
  • Python
    from sympy import primeomega
def afind(limit, startk=1):
    k = startk
    sk = "".join(str(i) for i in range(1, k))
    skr = "".join(str(i) for i in range(k-1, 0, -1))
    for k in range(startk, limit+1):
        sk += str(k)
        skr = str(k) + skr
        if primeomega(int(sk)) == primeomega(int(skr)):
            print(k, end=", ")
afind(23) # Michael S. Branicky, Feb 17 2022

Extensions

a(17) from Michael S. Branicky, Feb 19 2022
Showing 1-10 of 10 results.

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