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 A256652 Numbers D such that D^2 = A^4 + B^5 + C^6 has more than one solution in positive integers (A, B, C). 3
 1257, 32769, 262176, 262208, 1081344, 4198400, 16777217, 16809984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A subsequence of A255830. Sequences A256604 and A256603 are the analog for A180241 and A256091. Terms a(2) - a(8) have Hamming weight 2: 32769 = 2^15 + 1, 262176 = 2^18 + 2^5, 262208 = 2^18 + 2^6, 1081344 = 2^20 + 2^15, 4198400 = 2^22 + 2^12, 16777217 = 2^24 + 1, 16809984 = 2^24 + 2^15. Given D^2 = A^4+B^5+C^6, multiply by u^60, u>1, to get (u^30*D)^2 = (u^15*A)^4 + (u^12*B)^5 + (u^10*C)^6. If D is a solution then so is u^30*D. - Lars Blomberg, Apr 26 2015 Solutions for a(1)-a(8) as well as some larger terms: ..A1.....B1....C1......A2.....B2....C2..............D ..35......8.....6......32......2.....9...........1257 ..16......1....32......16.....64.....1..........32769 ..64......4....64.....512......4....16.........262176 ...8.....32....64.....512.....32.....4.........262208 1024.....64....64.....512....256....32........1081344 .480....240...160....2048....128....16........4198400 ...1.....32...256....4096.....32.....1.......16777217 1024.....64...256....4096....256....32.......16809984 .512......4..1024...32768......4....64.....1073741856 1024...4096.....8...32768....256.....8.....1073742336 4096...2048..1024...32768...2048...256.....1090519040 ...1..16384....64.....512..16384.....1....34359738369 4096..16384....16......64..16384...256....34359742464 4096..16384..1024...32768..16384...256....34376515584 .512...2048..4096..262144...2048....64....68719738880 ...1....256..8192....1024......1..8192...549755813889 1024...4096..8192...32768....256..8192...549756862464 - Lars Blomberg, Apr 26 2015 LINKS Table of n, a(n) for n=1..8. EXAMPLE (A, B, C) = (32, 2, 9): 32^4 + 2^5 + 9^6 = 1048576 + 32 + 531441 = 1580049 = 1257^2, and (A, B, C) = (35, 8, 6): 35^4 + 8^5 + 6^6 = 1500625 + 32768 + 46656 = 1580049 = 1257^2, so 1257 is a term. PROG (PARI) is_A256652(D, f=-1)={my(C=0, B, D2C6); while(1

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Last modified August 13 01:30 EDT 2024. Contains 375113 sequences. (Running on oeis4.)