A154874
Numbers k such that k^3 contains every digit exactly twice.
Original entry on oeis.org
2158479, 2190762, 2205528, 2219322, 2301615, 2330397, 2336268, 2345811, 2358828, 2359026, 2367609, 2388534, 2389119, 2389638, 2397132, 2428986, 2504736, 2524974, 2536152, 2583258, 2590125, 2607222, 2620827, 2622012, 2647866, 2649369, 2658636, 2671593
Offset: 1
2358828^3 = 13124683009764879552, which contains each digit 0..9 exactly twice.
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lim:=floor((10^20)^(1/3)): for j from ceil((10^19)^(1/3)) to lim do d:=convert(j^3,base,10): doubdig:=true: for k from 0 to 9 do if(numboccur(d,k)<>2)then doubdig:=false:break: fi: od: if(doubdig)then print(j); fi: od: # Nathaniel Johnston, May 28 2011
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With[{cmin=Ceiling[Surd[10^19,3]],cmax=Floor[Surd[10^20,3]]},Select[ Range[ cmin, cmax], Union[ DigitCount[#^3]]=={2}&]] (* Harvey P. Dale, Nov 17 2018 *)
A154875
Numbers k such that k^4 contains every digit exactly 3 times.
Original entry on oeis.org
17824719, 17940018, 18027474, 18197931, 18326025, 18798396, 18915888, 18929424, 19027455, 19149462, 19180275, 19196064, 19235673, 19311297, 19322913, 19324275, 19328322, 19455918, 19522575, 19757886, 19793664
Offset: 1
22807116 ^ 4 = 270571148920443982076865351936, which contains exactly 3 times of each digit 0-9.
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Select[Range[17824000,31608000],Union[Tally[IntegerDigits[#^4]][[All,2]]]=={3}&] (* Harvey P. Dale, Dec 24 2016 *)
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is(n) = my(v=vector(10), d=digits(n^4)); if(#d!=30,return(0)); for(i=1, #d, v[d[i]+1]++; if(v[d[i]+1] > 3, return(0))); 1 \\ David A. Corneth, Aug 19 2025
A154876
10-digit numbers n such that n^16 contains every digit exactly 16 times.
Original entry on oeis.org
8691229761, 8776040742, 8800099059, 8812428855, 8813522223, 8815323864, 8823675177, 8886940968, 9239038038, 9324907263, 9480130515, 9500938647, 9643844169, 9801034758, 9857840688, 9872688021, 9962545842, 9970902252
Offset: 1
8691229761^16=1059984945135973085116625441940958734567890938937942910046410302827750560860737374626331724228885721853160790705924439371252226476405367618058329962361885148161 means that 16th power of 8691229761 has all digit(0-9) each for 16 times exactly
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