A052093
a(n)^4 is the smallest fourth power whose decimal expansion digits occur with same frequency n.
Original entry on oeis.org
0, 207, 130398, 5694207, 426424828, 18304641024, 1002719491659
Offset: 1
207^4 = 1836036801 and digits 0,1,3,6 and 8 each occur twice.
A054212
a(n)^5 is the smallest fifth power whose decimal digits occur with same frequency n.
Original entry on oeis.org
0, 2955, 49995, 10365589, 75418384, 2592877410, 100661113419, 3989342709778, 2826734132736, 78074715540102
Offset: 1
2955^5 = 225313610074846875 and digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 each occur twice.
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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
A054213
Smallest fifth powers whose decimal expansion digits occur with same frequency n.
Original entry on oeis.org
0, 225313610074846875, 312343781246875156246875, 119665765800843104737370354851986949, 2439979134100773706931016420916722663424, 117195225794292252449115584887987847895470100000, 10334956410016814668660393585195309584134568401459883099, 1010431164918909763339703798486498718473866680301776494470190368
Offset: 1
2955^5 = 225313610074846875 and digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 each occur twice.
Showing 1-3 of 3 results.
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