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A334137 a(n) is the multiplicative inverse of A008514(n+1) modulo A008514(n).

%I A334137 #15 Aug 22 2025 20:03:41
%S A334137 0,10,19,267,338,1868,2069,948,7796,5245,22215,17198,3477,43855,21272,
%T A334137 95592,60647,186753,135194,45969,263049,139666,467532,301563,55386,
%U A334137 559636,241005,948261,543212,1508854,1001903,318414,1664590,828391,2587041,1575400,280143
%N A334137 a(n) is the multiplicative inverse of A008514(n+1) modulo A008514(n).
%H A334137 Daniel Hoyt, <a href="/A334137/b334137.txt">Table of n, a(n) for n = 0..10000</a>
%e A334137 For a(0), compute the inverse of 1^4 + 2^4 mod 0^4 + 1^4 which is 0 mod 1, since everything mod 1 is 0.
%e A334137 For a(1), compute the inverse of 2^4 + 3^4 mod 1^4 + 2^4. The inverse of 97 mod 17 (or 12 mod 17) is 10 mod 17 since 10*12 = 120 has remainder 1 mod 17.
%o A334137 (PARI)
%o A334137 f(n) = n^4 + (n+1)^4;
%o A334137 a(n) = lift(1/Mod(f(n+1), f(n)));
%o A334137 (Python)
%o A334137 import gmpy2
%o A334137 soc = [] # sum of 4d-centered cubes
%o A334137 a=0
%o A334137 b=1
%o A334137 for i in range(100):
%o A334137     c = a**4 + b**4
%o A334137     soc.append(c)
%o A334137     a += 1
%o A334137     b += 1
%o A334137 A334137 = []
%o A334137 for i in range(len(soc)-1):
%o A334137     c = gmpy2.invert(soc[i+1], soc[i])
%o A334137     A334137.append(int(c))
%o A334137 print(', '.join([str(x) for x in A334137]))
%Y A334137 Cf. A308215, A308217, A008514, A334121.
%K A334137 nonn,easy,changed
%O A334137 0,2
%A A334137 _Daniel Hoyt_, Apr 15 2020