1,1

{A000040}INTERSECT{A085739 Partial sums of A034953(n)}. {A000040}INTERSECT{SUM[i=1..n] A034953(i)}. {A000040}INTERSECT{SUM[i=1..n] A000217(A000040(i))}.

For triangular numbers T(n) = A000217(n) = n*(n+1)/2 we have:

a(1) = 3 because T(2) = T(prime(1)) = 3, and 3 is prime.

a(2) = 1729 because T(2) + ... T(31) = T(prime(1)) + ... + T(prime(11)) = 1719, which is prime.

a(3) = 3323 because T(2) + ... T(41) = T(prime(1)) + ... + T(prime(13)) = 3323, which is prime.

a(4) = 469303 because T(2) + ... + T(241) = 469303, which is prime.

a(5) = 605113 because T(2) + ... + T(269) = 605113, which is prime.

a(6) = 641969 because T(2) + ... + T(271) = 641969, which is prime.

a(7) = 1110587 because T(2) + ... + T(337) = 1110587, which is prime.

Cf. A000040, A000217, A034953, A085739.

Sequence in context: A060307 A119111 A118050 this_sequence A116994 A096730 A024047

Adjacent sequences: A116906 A116907 A116908 this_sequence A116910 A116911 A116912

easy,nonn,less

Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 16 2006