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

Author

Patrick De Geest, Feb 15 2000

Keywords

• nonn
• base
• hard
• more

Comments

Terms calculated by Jeff Heleen.

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

Examples

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

Links

• Patrick De Geest, Numbers whose digits occur with same frequency

Crossrefs

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

Programs

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

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