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 A344338 Smallest number that is the sum of two or more consecutive positive n-th powers in more than one way. 1
 9, 365, 33075 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(4) > 10^24. - Bert Dobbelaere, May 16 2021 Conjecture: no terms exist for n >= 4. - Jon E. Schoenfield, May 16 2021 LINKS EXAMPLE 9 = 2 + 3 + 4 = 4 + 5. 365 = 10^2 + 11^2 + 12^2 = 13^2 + 14^2. 33075 = 11^3 + 12^3 + 13^3 + 14^3 + 15^3 + 16^3 + 17^3 + 18^3 + 19^3 = 15^3 + 16^3 + 17^3 + 18^3 + 19^3 + 20^3. PROG (Python) N=3 # <== Adapt here import heapq sigma=1+2**N h=[(sigma, 1, 2)] nextcount=3 oldv, olds, oldl=0, 0, 0 while True: (v, s, l)=heapq.heappop(h) if v==oldv: break if v>=sigma: sigma += nextcount**N heapq.heappush(h, (sigma, 1, nextcount)) nextcount+=1 oldv, olds, oldl = v, s, l v-=s**N ; s+=1 ; l+=1 ; v+=l**N heapq.heappush(h, (v, s, l)) print("a(%d) = %d = sum(i^%d, i=%d..%d) = sum(i^%d, i=%d..%d)"% (N, v, N, olds, oldl, N, s, l)) # Bert Dobbelaere, May 16 2021 CROSSREFS Cf. A062681, A062682, A091414, A105441, A230718. Sequence in context: A132593 A162133 A197179 * A195888 A162084 A195518 Adjacent sequences: A344335 A344336 A344337 * A344339 A344340 A344341 KEYWORD nonn,bref,more,hard AUTHOR Ilya Gutkovskiy, May 15 2021 STATUS approved

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Last modified April 1 23:36 EDT 2023. Contains 361718 sequences. (Running on oeis4.)