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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

Table of n, a(n) for n=1..3.

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.)