cp's OEIS Frontend

A255830 Numbers D such that D^2 = A^4 + B^5 + C^6 for some positive integers A, B, C.

%I A255830 #20 Jul 19 2016 12:29:39
%S A255830 7,9,17,33,72,89,96,99,105,137,171,213,218,240,320,459,503,513,525,
%T A255830 616,761,792,833,1048,1127,1257,1369,1395,1536,1551,2025,2457,2600,
%U A255830 2610,3267,3312,3600,3681,4032,4100,4125,4128,4201,4901,4976,5001,5225,5880,5975,6167
%N A255830 Numbers D such that D^2 = A^4 + B^5 + C^6 for some positive integers A, B, C.
%C A255830 The sequence has the infinite subsequence (4^n*(2^n+16), n=0,1,2,...), with corresponding (A,B,C) = (2^(n+2),2^(n+1),2^n).
%C A255830 See A256652 for terms whose square has more than one representation of the given form. See A256613 for the subsequence of terms such that A^2 + B^3 + C^4 is a square, cf. A180241. See A256091 for the analog for sums of 3rd, 4th and 5th power.
%e A255830 (A, B, C) = (1, 4, 2) = 1^4 + 4^5 + 2^6 = 1 + 1024 + 64 = 1089 = 33^2, so 33 is a term.
%e A255830 (A, B, C) = (1, 4, 8) = 1^4 + 4^5 + 8^6 = 1 + 1024 + 262144 = 263169 = 513^2, so 513 is a term.
%o A255830 (PARI) is_A255830(D)=my(B,C=0,D2C6); while(1<D2C6=D^2-C++^6, B=0; while(0<D2C6-B++^5,ispower(D^2-C^6-B^5,4)&&return(1)))
%o A255830 for(D=1,9999,is_A255830(D)&&print1(D",")) \\ Converted to integer arithmetic by _M. F. Hasler_, May 01 2015
%Y A255830 Cf. A256091, A256613, A180241, A180242, A256652.
%K A255830 nonn
%O A255830 1,1
%A A255830 _M. F. Hasler_, Apr 06 2015
%E A255830 Inserted a(4)=33, a(18)=513 and removed doublet 1257 by _Lars Blomberg_, Apr 26 2015