A067503
Powers of 6 with digit sum also a power of 6.
Original entry on oeis.org
1, 6, 279936, 1679616, 10077696, 60466176, 13060694016, 4849687664788584363858837602739217760256, 174588755932389037098918153698611839369216
Offset: 1
A067505
Powers of 8 with digit sum also a power of 8.
Original entry on oeis.org
1, 8, 512, 68719476736, 76957043352332967211482500195592995713046365762627825523336510555167425334955489475418488779072100860950445293568
Offset: 1
Cf.
A067499,
A067500,
A067501,
A067502,
A067503,
A067504,
A067505,
A067506,
A067507,
A067508,
A067509,
A067510,
A067511.
A067504
Powers of 7 with digit sum also a power of 7.
Original entry on oeis.org
1, 7, 2401, 1977326743
Offset: 1
A067506
Powers of 9 with digit sum also a power of 9.
Original entry on oeis.org
1, 9, 81, 150094635296999121
Offset: 1
A067507
Powers of 2 with even digit sum.
Original entry on oeis.org
2, 4, 8, 64, 512, 2048, 8192, 16384, 32768, 131072, 2097152, 67108864, 4294967296, 8589934592, 68719476736, 137438953472, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664
Offset: 1
A067508
Powers of 4 with digit sum divisible by 4.
Original entry on oeis.org
4, 67108864, 68719476736, 1125899906842624, 18446744073709551616, 302231454903657293676544, 1208925819614629174706176, 4835703278458516698824704, 77371252455336267181195264, 316912650057057350374175801344, 5192296858534827628530496329220096
Offset: 1
A067509
Powers of 5 with digit sum divisible by 5.
Original entry on oeis.org
5, 390625, 9765625, 37252902984619140625, 9094947017729282379150390625, 227373675443232059478759765625, 3552713678800500929355621337890625, 2220446049250313080847263336181640625
Offset: 1
-
filter:= proc(n) convert(convert(n,base,10),`+`) mod 5 = 0 end proc:
select(filter, [seq(5^n,n=1..100)]); # Robert Israel, Apr 21 2020
A067510
Powers of 6 with digit sum divisible by 6.
Original entry on oeis.org
6, 1296, 279936, 1679616, 10077696, 60466176, 13060694016, 78364164096, 2821109907456, 16926659444736, 101559956668416, 3656158440062976, 789730223053602816, 4738381338321616896, 28430288029929701376
Offset: 1
Cf.
A067499,
A067500,
A067501,
A067502,
A067503,
A067504,
A067505,
A067506,
A067507,
A067508,
A067509.
-
select(n -> convert(convert(n,base,10),`+`)::even, [seq(6^i, i=1..100)]); # Robert Israel, Apr 20 2020
A067511
Powers of 7 with digit sum divisible by 7.
Original entry on oeis.org
7, 2401, 117649, 40353607, 1977326743, 9387480337647754305649, 65712362363534280139543, 459986536544739960976801, 15286700631942576193765185769276826401, 5243338316756303634461458718861951455543, 12589255298531885026341962383987545444758743
Offset: 1
Cf.
A067499,
A067500,
A067501,
A067502,
A067503,
A067504,
A067505,
A067506,
A067507,
A067508,
A067509,
A067510.
A359281
Numbers k such that the digit sum of 5^k is a power of 5.
Original entry on oeis.org
0, 1, 8, 208, 977, 1007, 4938, 24709, 24733, 24853, 124274, 3105928
Offset: 1
5^8 = 390625 and 3+9+0+6+2+5 = 5^2, so 8 is a term.
-
filter:= proc(n) local x;
x:= convert(convert(5^n,base,10),`+`);
x = 5^padic:-ordp(x,5)
end proc:
select(filter, [$0..10^5]); # Robert Israel, Jan 18 2023
-
Do[If[IntegerQ[Log[5, Plus @@ IntegerDigits[5^n]]], Print[n]], {n, 0, 150000}];
-
isok5(k) = (k==1) || (k==5) || (ispower(k,,&p) && (p==5));
isok(k) = isok5(sumdigits(5^k)); \\ Michel Marcus, Dec 24 2022
Showing 1-10 of 10 results.
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