A276170 Let n have j digits {d_j, d_(j-1), ..., d_2, d_1}. Sequence lists numbers n such that n = d_j^b_j + d_(j-1)^b_(j-1) + ... + d_2^b_2 + d_1^b_1 for some permutation {b_j, b_(j-1), ..., b_2, b_1} of the digits.

1, 1364, 3435, 4155, 4316, 4355, 17463, 48625, 63725, 78215, 117693, 136775, 137456, 137529, 164726, 184746, 196753, 264719, 326617, 326671, 397612, 423858, 516974, 637395, 652812, 653285, 653957, 687523, 834272, 936627, 1374962, 1617349, 1679812, 1683397, 1683514

Offset: 1

Author

Paolo P. Lava, Aug 23 2016

Keywords

• nonn
• base
• fini
• easy

Comments

0^0 is not admitted.

652812 is the first number with two essentially different permutations:

6^1 + 5^8 + 2^5 + 8^6 + 1^2 + 2^2 = 6^2 + 5^8 + 2^1 + 8^6 + 1^5 + 2^2 = 652812.

Examples

			One of the permutations of {1,3,6,4} is {6,1,4,3} and 1^6+3^1+6^4+4^3 = 1364.
		

Links

• Paolo P. Lava, First 100 terms with applicable permutations

Crossrefs

Cf. A046253, A166623.

Programs

Maple

with(combinat); P:= proc(q) local a,b,c,d,j,k,ok,n;
for n from 1 to q do ok:=1; d:=ilog10(n)+1; a:=convert(n,base,10); b:=permute(a,d);
for k from 1 to nops(b) do c:=0; for j from 1 to d do
if a[j]=0 and b[k][j]=0 then ok:=0; break; else c:=c+a[j]^b[k][j];  fi; od;
if ok=1 then if c=n then print(n); break; fi; fi; od; od; end: P(10^6);