cp's OEIS Frontend

A360297 a(n) = minimal positive k such that the sum of the primes prime(n) + prime(n+1) + ... + prime(n+k) is divisible by prime(n+k+1), or -1 if no such k exists.

%I A360297 #23 Apr 22 2025 16:26:13
%S A360297 1,3,7,11,26,20,27,52,1650,142,53,168234,212,7,13
%N A360297 a(n) = minimal positive k such that the sum of the primes prime(n) + prime(n+1) + ... + prime(n+k) is divisible by prime(n+k+1), or -1 if no such k exists.
%C A360297 In the first 100 terms there are twenty values for which a(n) is currently unknown; for all of these values a(n) is at least 10^9. These unknown terms are for n = 16, 22, 24, 34, 41, 42, 45, 48, 50, 54, 55, 62, 68, 70, 72, 75, 80, 87, 88, 98. In this same range the largest known value is a(76) = 749597506, where prime(76) = 383 leads to a sum of primes of 6173644601523754801 that is divisible by 16865554301.
%C A360297 See A360311 for the sum of the k+1 primes. See A360312 for prime(n+k+1).
%C A360297 a(16) > 10^10. - _Michael S. Branicky_, Feb 19 2025
%C A360297 a(16) > 10^12. - _Michael S. Branicky_, Apr 22 2025
%H A360297 Scott R. Shannon, <a href="/A360297/a360297.txt">Terms for n = 1..100</a>. The terms currently unknown are set to -1.
%e A360297 a(1) = 1 as prime(1) + prime(2) = 2 + 3 = 5, which is divisible by prime(3) = 5.
%e A360297 a(4) = 11 as prime(4) + ... + prime(15) = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 318, which is divisible by prime(16) = 53.
%o A360297 (Python)
%o A360297 from sympy import prime, nextprime
%o A360297 def A360297(n):
%o A360297     p = prime(n)
%o A360297     q = nextprime(p)
%o A360297     s, k = p+q, 1
%o A360297     while s%(q:=nextprime(q)):
%o A360297         k += 1
%o A360297         s += q
%o A360297     return k # _Chai Wah Wu_, Feb 03 2023
%Y A360297 Cf. A360311, A360312, A000040, A007504, A332542, A332580.
%K A360297 nonn,more
%O A360297 1,2
%A A360297 _Scott R. Shannon_, Feb 02 2023