A054212 a(n)^5 is the smallest fifth power whose decimal digits occur with same frequency n.

0, 2955, 49995, 10365589, 75418384, 2592877410, 100661113419, 3989342709778, 2826734132736, 78074715540102

Offset

1,2

Comments

Terms calculated by Jeff Heleen.

Next term > 2.5*10^17 - Frank A. Stevenson, Feb 02 2024

Links

Table of n, a(n) for n=1..10.

Patrick De Geest, Numbers whose digits occur with same frequency

Example

2955^5 = 225313610074846875 and digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 each occur twice.

Prog

(Python)
def agen(POW=5):
  n = 1
  while True:
    k = 0
    while True:
      kpowstr = str(pow(k, POW))
      q, r = divmod(len(kpowstr), n)
      if r == 0:
        ok = True
        for d in set(kpowstr):
          if kpowstr.count(d) != n:
            ok = False; break
        if ok: break
        k += 1
      else: # go to next multiple of n digits: (q+1)*n
        k = max(k+1, int((10**((q+1)*n-1))**(1/POW)))
    yield k
    n += 1
g = agen() # call with POW=4, 3, 2 for A052093, A052071, A052069
print([next(g) for n in range(1, 5)]) # Michael S. Branicky, Dec 17 2020

Crossrefs

Cf. A054213, A052093, A052094, A052069, A052071.

Sequence in context: A178273 A289562 A054833 * A179138 A236005 A107534

Adjacent sequences: A054209 A054210 A054211 * A054213 A054214 A054215

Keyword

nonn,base,hard,more

Author

Patrick De Geest, Feb 15 2000

Extensions

Offset corrected by Michel Marcus, Aug 12 2015

a(7)-a(8) from Michael S. Branicky, Dec 17 2020

a(9)-a(10) from Frank A. Stevenson, Jan 02 2024

Status

approved