A096380 Differences between the sum of the first three primes and the fourth prime in consecutive prime quadruples.

3, 4, 10, 14, 22, 26, 30, 40, 46, 56, 66, 74, 78, 84, 98, 106, 116, 126, 132, 140, 146, 154, 168, 184, 194, 202, 206, 202, 218, 234, 256, 258, 274, 282, 294, 304, 314, 324, 338, 342, 358, 368, 382, 378, 384, 406, 432, 446, 450, 460, 462, 474, 486, 502, 518, 526

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = prime(n) + prime(n+1) + prime(n+2) - prime(n+3).

a(n) = Sum_{k=0..3} (-1)^A121262(k+1) * prime(n+k). - Wesley Ivan Hurt, Nov 22 2023

Mathematica

Total[Take[#, 3]]-Last[#]&/@Partition[Prime[Range[100]], 4, 1] (* Harvey P. Dale, May 14 2011 *)

Prog

(PARI) g(n)=for(x=1, n, print1(prime(x)+prime(x+1)+prime(x+2)-prime(x+3)", "))

Crossrefs

Cf. A000040, A121262.

Sequence in context: A143372 A035594 A167273 * A309478 A329805 A071019

Adjacent sequences: A096377 A096378 A096379 * A096381 A096382 A096383

Keyword

nonn,easy

Author

Cino Hilliard, Aug 04 2004

Extensions

Offset set to 1 by Wesley Ivan Hurt, Nov 22 2023

Status

approved