login
Numbers k such that abs(S(k)) = A008347(k) is prime, where S(k) = S(k-1) + A000040(k)*(-1)^k; S(0) = 0.
1

%I #8 Oct 04 2024 11:22:50

%S 1,4,6,8,10,12,18,28,32,38,42,46,50,52,54,64,68,70,72,74,76,86,88,98,

%T 100,110,126,128,130,140,146,152,162,192,202,214,226,242,252,258,264,

%U 270,290,294,304,308,314,316,320,322,332,342,348,352,358,360

%N Numbers k such that abs(S(k)) = A008347(k) is prime, where S(k) = S(k-1) + A000040(k)*(-1)^k; S(0) = 0.

%C The sequence include as first term the only case where S(k) = -1 times a prime: S(1) = -2.

%e S(3) = ((0+2*-1)+3*1)+5*-1 = -4, S(4) = -4 + 7*1 = 3 is prime, hence 4 is a term.

%e S(5) = ((((0+2*-1)+3*1)+5*-1)+7*1)+11*-1 = -8, S(6) = -8 + 13*1 = 5 is prime, hence 6 is a term.

%t S=0; Do[S=S+Prime[n]*(-1)^n; If[PrimeQ[S]==True, Print[n]], {n, 1, 10^3, 1}]

%Y Cf. A008347, A066033, A000040.

%K nonn

%O 1,2

%A _Manuel Valdivia_, Oct 03 2007