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%I #9 Nov 22 2023 11:04:14
%S 3,4,10,14,22,26,30,40,46,56,66,74,78,84,98,106,116,126,132,140,146,
%T 154,168,184,194,202,206,202,218,234,256,258,274,282,294,304,314,324,
%U 338,342,358,368,382,378,384,406,432,446,450,460,462,474,486,502,518,526
%N Differences between the sum of the first three primes and the fourth prime in consecutive prime quadruples.
%C There are occurrences where the next term is less than the current term. Conjecture: The number of occurrences where the current term exceeds the next term is infinite.
%F a(n) = prime(n) + prime(n+1) + prime(n+2) - prime(n+3).
%F a(n) = Sum_{k=0..3} (-1)^A121262(k+1) * prime(n+k). - _Wesley Ivan Hurt_, Nov 22 2023
%t Total[Take[#,3]]-Last[#]&/@Partition[Prime[Range[100]],4,1] (* _Harvey P. Dale_, May 14 2011 *)
%o (PARI) g(n)=for(x=1,n,print1(prime(x)+prime(x+1)+prime(x+2)-prime(x+3)","))
%Y Cf. A000040, A121262.
%K nonn,easy
%O 1,1
%A _Cino Hilliard_, Aug 04 2004
%E Offset set to 1 by _Wesley Ivan Hurt_, Nov 22 2023
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