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 1-7 of 7 results.

A256359 Numbers n such that there is at least one base b in which n is a multiple-digit narcissistic number.

Original entry on oeis.org

5, 8, 10, 13, 17, 18, 20, 25, 26, 28, 29, 32, 35, 37, 40, 41, 43, 45, 50, 52, 53, 55, 58, 61, 62, 65, 68, 72, 80, 82, 83, 85, 90, 92, 97, 98, 99, 101, 104, 109, 113, 117, 118, 122, 125, 126, 127, 128, 133, 134, 136, 145, 146, 148, 152, 153, 160, 162
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Mar 26 2015

Keywords

Examples

			a(1) = 5 because this is the first number that is a multiple-digit narcissistic number in at least one base (3).

Links

Crossrefs

Cf. A005188.
Cf. A256360, A256361, A256362, A256363, A256364, A256365 (1 to 6 bases).
Cf. A256459 (first occurrences).

Programs

  • Mathematica
    Select[Range@ 162, Function[k, AnyTrue[Range[2, k], Total[#^Length@ #] &@ IntegerDigits[k, #] == k &]]] (* Version 10, or *)
Select[Range@ 162, Function[k, Total@ Boole[Total[#^Length@ #] &@ IntegerDigits[k, #] == k & /@ Range[2, k]] > 0]] (* Michael De Vlieger, Apr 30 2016 *)
  • PARI
    for(n=3,1000000, k=0; for(z=2,n, y=n; j=0; L=List(); until(y==0, x=y%z; j++; listinsert(L,x,j); while(!((y%z)==0), y--); y=y/z); t=0; for(p=1,j, t+=L[p]^j); if(n==t, k++)); if(k>0, print1(n,", ")))

A256360 Numbers that are multiple-digit narcissistic numbers in exactly one base.

Original entry on oeis.org

5, 8, 10, 13, 18, 20, 25, 26, 32, 35, 37, 40, 41, 43, 52, 53, 55, 58, 61, 62, 65, 68, 72, 80, 82, 83, 90, 92, 97, 98, 99, 101, 104, 109, 113, 117, 118, 122, 127, 128, 134, 146, 148, 152, 162, 170, 173, 178, 180, 181, 185, 190, 197, 205, 221, 225
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Mar 26 2015

Keywords

Comments

See A258273 for the corresponding bases.

Examples

			a(1) = 5 because this is the first number that is a multiple-digit narcissistic number in exactly one base (3).

Links

Crossrefs

Cf. A005188.
Cf. A256359 (every number of bases).
Cf. A256361, A256362, A256363, A256364, A256365 (2 to 6 bases).
Cf. A256459 (first occurrences).

Programs

  • PARI
    for(n=3, 1000000, k=0; for(z=2, n, y=n; j=0; L=List(); until(y==0, x=y%z; j++; listinsert(L, x, j); while(!((y%z)==0), y--); y=y/z); t=0; for(p=1, j, t+=L[p]^j); if(n==t, k++)); if(k==1, print1(n, ", ")))

A256361 Numbers that are multiple-digit narcissistic numbers in exactly two bases.

Original entry on oeis.org

17, 28, 29, 45, 50, 85, 126, 133, 136, 145, 153, 160, 200, 245, 250, 260, 261, 265, 353, 365, 371, 405, 425, 442, 450, 490, 514, 520, 533, 585, 605, 650, 666, 680, 738, 800, 855, 925, 936, 1000, 1025, 1105, 1225, 1233, 1250, 1280
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Mar 26 2015

Keywords

Examples

			a(1) = 17 because this is the first number that is a multiple-digit narcissistic number in exactly two bases (3 and 13).

Links

Crossrefs

Cf. A005188.
Cf. A256359 (every number of bases).
Cf. A256360, A256362, A256363, A256364, A256365 (1, 3 to 6 bases).
Cf. A256459 (first occurrences).

Programs

  • PARI
    for(n=3, 1000000, k=0; for(z=2, n, y=n; j=0; L=List(); until(y==0, x=y%z; j++; listinsert(L, x, j); while(!((y%z)==0), y--); y=y/z); t=0; for(p=1, j, t+=L[p]^j); if(n==t, k++)); if(k==2, print1(n, ", ")))

A256362 Numbers that are multiple-digit narcissistic numbers in exactly three bases.

Original entry on oeis.org

125, 325, 370, 793, 845, 1125, 1445, 2080, 2125, 2925, 3125, 3200, 3725, 3757, 5050, 5265, 6125, 6250, 6845, 7605, 8125, 8405, 10125, 10261, 10440, 10625, 11250, 13005, 13690, 14365, 15125, 15925, 18785, 22100
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Mar 26 2015

Keywords

Examples

			a(1) = 125 because this is the first number that is a multiple-digit narcissistic number in exactly three bases (12, 23 and 57).

Links

Crossrefs

Cf. A005188.
Cf. A256359 (every number of bases).
Cf. A256360, A256361, A256363, A256364, A256365 (1, 2, 4, 5 and 6 bases).
Cf. A256459 (first occurrences).

Programs

  • PARI
    for(n=3, 1000000, k=0; for(z=2, n, y=n; j=0; L=List(); until(y==0, x=y%z; j++; listinsert(L, x, j); while(!((y%z)==0), y--); y=y/z); t=0; for(p=1, j, t+=L[p]^j); if(n==t, k++)); if(k==3, print1(n, ", ")))

A256364 Numbers that are multiple-digit narcissistic numbers in exactly five bases.

Original entry on oeis.org

274625, 465125, 528125, 710645, 912925, 983125
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Mar 30 2015

Keywords

Examples

			a(1) = 274625 because this is the first number that is a multiple-digit narcissistic number in exactly five bases (528, 603, 1318, 1958 and 4217).

Links

Crossrefs

Cf. A005188.
Cf. A256359 (every number of bases).
Cf. A256360, A256361, A256362, A256363, A256365 (1 to 4 and 6 bases).
Cf. A256459 (first occurrences).

Programs

  • PARI
    for(n=3, 1000000, k=0; for(z=2, n, y=n; j=0; L=List(); until(y==0, x=y%z; j++; listinsert(L, x, j); while(!((y%z)==0), y--); y=y/z); t=0; for(p=1, j, t+=L[p]^j); if(n==t, k++)); if(k==5, print1(n, ", ")))

A256365 Numbers that are multiple-digit narcissistic numbers in exactly six bases.

Original entry on oeis.org

36125, 190125, 444925
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Mar 30 2015

Keywords

Examples

			a(1) = 36125 because this is the first number that is a multiple-digit narcissistic number in exactly six bases (193, 212, 327, 423, 1057 and 7187).

Links

Crossrefs

Cf. A005188.
Cf. A256359 (every number of bases).
Cf. A256360, A256361, A256362, A256363, A256364 (1 to 5 bases).
Cf. A256459 (first occurrences).

Programs

  • PARI
    for(n=3, 1000000, k=0; for(z=2, n, y=n; j=0; L=List(); until(y==0, x=y%z; j++; listinsert(L, x, j); while(!((y%z)==0), y--); y=y/z); t=0; for(p=1, j, t+=L[p]^j); if(n==t, k++)); if(k==6, print1(n, ", ")))

A256459 Least number that is a multiple-digit narcissistic number in exactly n bases.

Original entry on oeis.org

5, 17, 125, 4901, 274625, 36125
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Mar 30 2015

Keywords

Examples

			a(3) = 125 because this is the least number that is a multiple-digit narcissistic number in exactly three bases (12, 23 and 57).

Links

Crossrefs

Cf. A005188.
Cf. A256359 (every number of bases).
Cf. A256360, A256361, A256362, A256363, A256364, A256365 (1 to 6 bases).

Programs

  • PARI
    b=0; until(b==6, b++; n=2; until(k==b, n++; k=0; for(z=2, n, y=n; j=0; L=List(); until(y==0, x=y%z; j++; listinsert(L, x, j); while(!((y%z)==0), y--); y=y/z); t=0; for(p=1, j, t+=L[p]^j); if(n==t, k++)); if(k==b, print1(n, " "))))
Showing 1-7 of 7 results.

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