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.

A077377 Squarefree numbers whose external digits form a squarefree number.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 105, 107, 109, 110, 111, 113
Offset: 1

Views

Author

Amarnath Murthy, Nov 06 2002

Keywords

Links

Crossrefs

Cf. A005117, A077376, A077378, A077379, A077380.

Programs

  • Mathematica
    A077377Q[k_] := SquareFreeQ[k] && (k < 10 || SquareFreeQ[FromDigits[IntegerDigits[k][[{1, -1}]]]]);
Select[Range[200], A077377Q] (* Paolo Xausa, Feb 19 2025 *)
  • PARI
    list(lim)=my(v=List(),n,t); for(d=0,logint(lim\=1,10), t=10^d; forsquarefree(k=t,min(10*t-1,lim), if(issquarefree(k[1]\t*10 + k[1]%10), listput(v,k[1])))); Vec(v) \\ Charles R Greathouse IV, Feb 14 2018

Extensions

a(1) inserted by Charles R Greathouse IV, Feb 14 2018

A077378 Squarefree numbers whose external as well as internal digits form a squarefree number.

Original entry on oeis.org

123, 127, 129, 130, 131, 133, 134, 137, 139, 151, 154, 155, 157, 159, 161, 163, 165, 167, 170, 173, 174, 177, 179, 221, 222, 223, 226, 229, 231, 233, 239, 251, 253, 259, 262, 263, 266, 269, 271, 273, 321, 323, 327, 329, 330, 331, 334, 335, 337, 339, 353, 354, 355, 357, 358
Offset: 1

Views

Author

Amarnath Murthy, Nov 06 2002

Keywords

Comments

Here 1 is treated as not squarefree. - Andrew Howroyd, Sep 19 2024

Links

Crossrefs

Intersection of A077376 and A077377.
Cf. A005117, A077379, A077380.

Programs

  • Mathematica
    A077378Q[k_] := k >= 100 && SquareFreeQ[k] && SquareFreeQ[FromDigits[#[[{1, -1}]]]] && FromDigits[#[[2;; -2]]] > 1 && SquareFreeQ[FromDigits[#[[2;; -2]]]] & [IntegerDigits[k]];
Select[Range[500], A077378Q] (* Paolo Xausa, Feb 19 2025 *)
  • PARI
    isok(k)={if(issquarefree(k) && k>=100, my(b=10^logint(k,10), m=k%b\10); m!=1 && issquarefree(m) && issquarefree(k\b*10+k%10), 0)} \\ Andrew Howroyd, Sep 19 2024

Extensions

Offset changed and a(29) onwards from Andrew Howroyd, Sep 19 2024

A077380 Largest n-digit squarefree number whose internal as well as external digits form a squarefree number, or 0 if no such number exists.

Original entry on oeis.org

0, 0, 977, 9977, 99987, 999987, 9999987, 99999977, 999999985, 9999999987, 99999999987, 999999999987, 9999999999987, 99999999999987, 999999999999987, 9999999999999987, 99999999999999987, 999999999999999987
Offset: 1

Views

Author

Amarnath Murthy, Nov 06 2002

Keywords

Crossrefs

Cf. A077376, A077377, A077378, A077379.

Programs

  • Maple
    with(numtheory) ; A077380 := proc(n) local anmax,leadd,edit,idit ; anmax := 10^n-1 ; while anmax >= 10^(n-1) do leadd := floor(anmax/10^(n-1)) ; edit := 10*leadd + ( anmax mod 10 ); idit := floor(anmax/10) -leadd*10^(n-2) ; if issqrfree(anmax) and issqrfree(edit) and issqrfree(idit) then RETURN(anmax) ; fi ; anmax := anmax-1 ; od ; RETURN(0) ; end: printf("0,") ; for n from 2 to 30 do printf("%d,",A077380(n)) ; od ; # R. J. Mathar, Sep 26 2006

Extensions

More terms from R. J. Mathar, Sep 26 2006

A077376 Squarefree numbers whose internal digits form a squarefree number.

Original entry on oeis.org

122, 123, 127, 129, 130, 131, 133, 134, 137, 138, 139, 151, 154, 155, 157, 158, 159, 161, 163, 165, 166, 167, 170, 173, 174, 177, 178, 179, 221, 222, 223, 226, 227, 229, 230, 231, 233, 235, 237, 238, 239, 251, 253, 254, 255, 257, 258, 259, 262, 263, 265, 266
Offset: 1

Views

Author

Amarnath Murthy, Nov 06 2002

Keywords

Comments

Here 1 is treated as not squarefree. - Harvey P. Dale, Jul 22 2012

Crossrefs

Cf. A077377, A077378, A077379, A077380.

Programs

  • Mathematica
    sf2Q[n_]:=Module[{c=FromDigits[Most[Rest[IntegerDigits[n]]]]},c!=1&&SquareFreeQ[ n]&&SquareFreeQ[c]]; Select[Range[100,300],sf2Q] (* Harvey P. Dale, Jul 22 2012 *)

Extensions

More terms from Harvey P. Dale, Jul 22 2012
Offset changed by Andrew Howroyd, Sep 19 2024
Showing 1-4 of 4 results.

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