A211199
Sum of the 16th powers of the decimal digits of n.
Original entry on oeis.org
0, 1, 65536, 43046721, 4294967296, 152587890625, 2821109907456, 33232930569601, 281474976710656, 1853020188851841, 1, 2, 65537, 43046722, 4294967297, 152587890626, 2821109907457, 33232930569602, 281474976710657, 1853020188851842, 65536, 65537, 131072, 43112257
Offset: 0
a(14) = 1^16 + 4^16 = 4294967297 = 641 * 6700417.
A338235
Numbers k such that k + the sum of the 4th powers of the decimal digits of k is a square.
Original entry on oeis.org
20, 47, 104, 113, 228, 255, 333, 544, 632, 743, 1054, 1122, 1518, 1762, 1901, 2071, 3617, 4317, 4432, 4456, 4513, 4557, 4727, 4927, 5000, 5058, 5080, 5173, 5473, 5847, 6047, 6767, 6832, 7247, 7408, 7453, 7487, 7518, 7921, 7997, 8127, 8958, 9208, 9487, 10917
Offset: 1
20 is a member since 2^4 + 0^4 + 20 = 6^2,
47 is a member since 4^4 + 7^4 + 47 = 52^2,
104 is a member since 1^4 + 0^4 + 4^4 = 104 = 19^2,
113 is a member since 1^4 + 1^4 + 3^4 + 113 = 14^2.
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filter:= proc(n) local L,k;
issqr(n + add(t^4, t=convert(n,base,10)))
end proc:
select(filter, [$1..20000]); # Robert Israel, Jan 30 2021
A355708
Irregular triangle read by rows in which row n lists the possible periods for the iterations of the map sum of n-th powers of digits.
Original entry on oeis.org
1, 1, 8, 1, 2, 3, 1, 2, 7, 1, 2, 4, 6, 10, 12, 22, 28, 1, 2, 3, 4, 10, 30, 1, 2, 3, 6, 12, 14, 21, 27, 30, 56, 92, 1, 25, 154, 1, 2, 3, 4, 8, 10, 19, 24, 28, 30, 80, 93, 1, 6, 7, 17, 81, 123
Offset: 1
Triangle begins:
1;
1, 8;
1, 2, 3;
1, 2, 7;
1, 2, 4, 6, 10, 12, 22, 28;
1, 2, 3, 4, 10, 30;
1, 2, 3, 6, 12, 14, 21, 27, 30, 56, 92;
1, 25, 154;
1, 2, 3, 4, 8, 10, 19, 24, 28, 30, 80, 93;
1, 6, 7, 17, 81, 123;
...
A383349
Numbers that have the same set of digits as the sum of 4th powers of its digits.
Original entry on oeis.org
0, 1, 488, 668, 686, 848, 866, 884, 1346, 1364, 1436, 1463, 1634, 1643, 2088, 2556, 2565, 2655, 2808, 2880, 3146, 3164, 3416, 3461, 3614, 3641, 4136, 4163, 4316, 4361, 4479, 4497, 4613, 4631, 4749, 4794, 4947, 4974, 5256, 5265, 5526, 5562, 5625, 5652, 6134, 6143
Offset: 1
488 and 4^4 + 8^4 + 8^4 = 8448 have the same set of digits {4,8}, so 488 is a term.
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q[k_] := Module[{d = IntegerDigits[k]}, Union[d] == Union[IntegerDigits[Total[d^4]]]]; Select[Range[0, 7000], q] (* Amiram Eldar, Apr 24 2025 *)
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isok(k) = my(d=digits(k)); Set(d) == Set(digits(sum(i=1, #d, d[i]^4))); \\ Michel Marcus, Apr 24 2025
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def ok(n): return set(s:=str(n)) == set(str(sum(int(d)**4 for d in s)))
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, Apr 24 2025
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