A265449 Palindromes that are the sums of consecutive fourth powers.
0, 1, 353, 979, 14641, 16561, 998899, 2138312, 104060401, 1004006004001, 10004000600040001, 85045192129154058, 100004000060000400001, 1000004000006000004000001, 10000004000000600000040000001
Offset: 1
Examples
353 = 2^4 + 3^4 + 4^4 979 = 1^4 + 2^4 + 3^4 + 4^4 + 5^4 16561 = 9^4 + 10^4 998899 = 19^4 +...+ 23^4 2138312 = 10^4 +...+ 25^4 85045192129154058 = 5582^4 +...+ 5666^4
Programs
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Python
import heapq def ispal(n): s = str(n); return s == s[::-1] def afind(): print("0, ") # special case N, T = 4, 1 # power, min number of terms sigma = sum(i**N for i in range(1, T+1)) h = [(sigma, 1, T)] nextcount = T + 1 while True: (v, s, l) = heapq.heappop(h) if ispal(v): print(f"{v}, [= Sum_{{i = {s}..{l}}} i^{N}]") if v >= sigma: sigma += nextcount**N heapq.heappush(h, (sigma, 1, nextcount)) nextcount += 1 v -= s**N; s += 1; l += 1; v += l**N heapq.heappush(h, (v, s, l)) afind() # Michael S. Branicky, May 16 2021 after Bert Dobbelaere in A344338
Extensions
a(13)-a(15) from Giovanni Resta, Aug 27 2019
Comments