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

Author

Chai Wah Wu, Jan 29 2016

Keywords

• nonn
• base
• more

Comments

Subsequence of A217844 and supersequence of A186080.

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
		

Crossrefs

Cf. A186080, A217844.

Programs

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