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.

A253601 Numbers such that the smallest exponent for n and n^k to have common digits is 3.

Original entry on oeis.org

4, 9, 17, 18, 24, 29, 33, 34, 38, 39, 44, 54, 57, 58, 59, 62, 67, 72, 79, 84, 88, 94, 144, 158, 173, 194, 209, 212, 224, 237, 238, 244, 247, 253, 257, 259, 307, 313, 314, 333, 334, 338, 349, 353, 359, 377, 388, 404, 409, 424, 437, 444, 447, 449, 454, 459, 467
Offset: 1

Views

Author

Michel Marcus, Jan 05 2015

Keywords

Examples

			4^2=16 has no digits in common with 4, but 4^3=64 has some, so 4 is in the sequence.

Links

Crossrefs

Cf. A103173, A189056, A253600, A253602.

Programs

  • PARI
    a253600(n) = {sd = Set(vecsort(digits(n))); k=2; while (#setintersect(sd, Set(vecsort(digits(n^k)))) == 0, k++); k;}
isok(n) = a253600(n) == 3;
  • PARI
    is(n) = my(d(k)=Set(digits(n^k))); !#setintersect(d(1), d(2)) && #setintersect(d(1), d(3)) \\ Iain Fox, Aug 07 2018

A373203 a(n) = minimum k>1 such that n^k contains all distinct decimal digits of n.

Original entry on oeis.org

2, 2, 5, 5, 3, 2, 2, 5, 5, 3, 2, 2, 3, 5, 4, 6, 5, 5, 5, 7, 5, 3, 4, 7, 3, 2, 8, 2, 5, 3, 5, 4, 3, 3, 3, 6, 6, 5, 4, 3, 3, 6, 7, 4, 3, 4, 4, 4, 4, 3, 2, 3, 7, 5, 3, 2, 3, 5, 5, 3, 2, 3, 5, 2, 2, 3, 2, 3, 4, 5, 5, 3, 3, 3, 2, 3, 2, 5, 5, 5, 5
Offset: 0

Views

Author

James C. McMahon, May 27 2024

Keywords

Examples

			For n=12, a(12)=3 because 12^3=1728 contains all decimal digits of n. Compare to A253600(12)=2 because 12^2=144 contains any digit of n.

Links

Crossrefs

Cf. A045537, A111442, A253600.

Programs

  • Mathematica
    seq={}; Do[k=1;Until[ContainsAll[IntegerDigits[n^k],IntegerDigits[n] ],k++];AppendTo[seq,k] ,{n,0,80}];seq
  • PARI
    a(n) = my(k=2, d=Set(digits(n))); while(setintersect(Set(digits(n^k)), d) != d, k++); k; \\ Michel Marcus, Jun 01 2024
  • Python
    from itertools import count
def a(n):
    s = set(str(n))
    return next(k for k in count(2) if s <= set(str(n**k)))
print([a(n) for n in range(81)]) # Michael S. Branicky, May 27 2024

Formula

A253600(n) <= a(n) <= A045537(n). - Michael S. Branicky, May 28 2024
A111442(n) = n^a(n).

A253602 Numbers n such that the smallest exponent k for n and n^k to have common digits is 4.

Original entry on oeis.org

22, 47, 92, 157, 187, 188, 192, 552, 558, 577, 707, 772, 922, 2522, 8338, 17177, 66888, 575757, 929522, 1717177, 8888588
Offset: 1

Views

Author

Michel Marcus, Jan 05 2015

Keywords

Examples

			22^2=484 and 22^3=10648 have no digits in common with 22, but 22^4=234256 has some, so 22 is in the sequence.

Crossrefs

Cf. A029790, A103173, A189056, A253600, A253601.

Programs

  • PARI
    a253600(n) = {sd = Set(vecsort(digits(n))); k=2; while (#setintersect(sd, Set(vecsort(digits(n^k)))) == 0, k++); k;}
isok(n) = a253600(n) == 4;

A373291 Least perfect power of n containing some decimal digit of n.

Original entry on oeis.org

1, 32, 243, 64, 25, 36, 16807, 32768, 729, 100, 121, 144, 169, 196, 225, 256, 4913, 5832, 361, 400, 441, 234256, 529, 13824, 625, 676, 729, 784, 24389, 900, 961, 1024, 35937, 39304, 1225, 1296, 1369, 54872, 59319, 1600
Offset: 1

Views

Author

James C. McMahon, May 30 2024

Keywords

Comments

"Perfect power of n" here means n^k with k>1. The sequence gives the value of n^k, not the value of k. - N. J. A. Sloane, May 31 2024

Examples

			For n=12, 12^2=144 contains digit 1 from n so that a(12) = 144.

Crossrefs

Cf. A111442, A253600.

Programs

  • Mathematica
    seq={}; Do[k=1;  Until[  ContainsAny[IntegerDigits[n],IntegerDigits[n^k] ],k++  ];AppendTo[seq,n^k] ,{n,40}];seq
  • PARI
    a(n) = my(sd = Set(vecsort(digits(n))), k=2); while (#setintersect(sd, Set(vecsort(digits(n^k)))) == 0, k++); n^k; \\ Michel Marcus, May 31 2024

Formula

a(n) = n^A253600(n).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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