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 A359055 Numbers that can be represented in more than one way as the sum of cubes of three distinct positive numbers in arithmetic progression. 1
 5643, 12384, 31977, 45144, 99072, 123849, 152361, 153792, 255816, 259776, 269739, 274968, 334368, 361152, 477576, 500445, 705375, 792576, 863379, 912339, 928017, 950931, 990792, 1090584, 1218888, 1230336, 1548000, 1629144, 1700424, 1737252, 1799523, 1813512, 1935549, 1941192, 2046528, 2078208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers k such that there are at least two pairs of positive numbers (a,d) such that k = a^3 + (a+d)^3 + (a+2d)^3. The first term that has three such representations is 255816 = 8^3 + 34^3 + 60^3 = 18^3 + 38^3 + 58^3 = 43^3 + 44^3 + 45^3. 346380489216 has four such representations: 1188^3 + 3888^3 + 6588^3, 1728^3 + 4104^3 + 6480^3, 4248^3 + 4824^3 + 5400^3 and 4665^3 + 4864^3 + 5063^3. It might not be the first. LINKS Robert Israel, Table of n, a(n) for n = 1..2500 R. Israel et al, Sum of cubes of three positive integers in arithmetic progression in four ways?, Mathematics StackExchange, Dec. 2022. EXAMPLE a(1) = 5643 is a term because 5643 = 1^3 + (1+8)^3 + (1+2*8)^3 = 6^3 + (6+5)^3 + (6+2*5)^3. MAPLE N:= 10^7: # to get terms <= N S:= {}: S2:= {}: for a from 1 while a^3 + (a+1)^3 + (a+2)^3 <= N do for d from 1 do x:= a^3 + (a+d)^3 + (a+2*d)^3; if x > N then break fi; if member(x, S) then S2:= S2 union {x} fi; S:= S union {x} od od: sort(convert(S, list)); CROSSREFS Cf. A306213. Sequence in context: A247402 A339961 A332738 * A184080 A234401 A203726 Adjacent sequences: A359052 A359053 A359054 * A359056 A359057 A359058 KEYWORD nonn AUTHOR Robert Israel, Dec 14 2022 STATUS approved

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Last modified September 16 17:53 EDT 2024. Contains 375976 sequences. (Running on oeis4.)