A270541 a(n) = A001359(n) - A001359(n+1) - A001359(n+2) + A001359(n+3).

4, 6, 6, 6, 0, 12, -6, 0, 6, 0, 0, -24, 18, 6, 0, 0, 0, 24, 42, -24, -42, 48, 18, -30, -30, -6, 0, 126, -6, -144, 18, 18, 108, -12, -120, 0, 12, 48, 48, -12, -66, -36, 6, 96, 6, -78, -18, 90, 6, -72, 18, -24, 36, 60, -60, -30, 12, -6, 12, 6, -24, -30, 12, -12, 78, 18, -54, 0, 0, 138, 0, -102, -12, -42

Offset: 1

Author

Altug Alkan, Mar 18 2016

Keywords

• sign

Comments

6*k appears for the form of a(n) for n > 1.

What is the most repeated value of a(n)?

See A270535 for the position of 0's in this sequence.

Examples

			a(1) = 4 because a(1) = A001359(1) - A001359(2) - A001359(3) + A001359(4) = 3 - 5 - 11 + 17 = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A006512, A014574, A053319.

Programs

Mathematica

s = Select[Prime@Range[10^6], PrimeQ[# + 2] &]; Table[s[[n]] - s[[n + 1]] - s[[n + 2]] + s[[n + 3]], {n, 74}] (* Michael De Vlieger, Mar 19 2016, after Robert G. Wilson v at A001359 *)
#[[1]]-#[[2]]-#[[3]]+#[[4]]&/@Partition[Select[Partition[Prime[Range[400]],2,1],#[[2]]-#[[1]]==2&][[;;,1]],4,1] (* Harvey P. Dale, Jun 14 2025 *)

PARI

t(n, p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
a(n) = t(n) + t(n+3) - t(n+1) - t(n+2);
for(n=1, 200, print1(a(n), ", "));

Formula

a(n) = A053319(n+2) - A053319(n).