A368880 Primes in A024528.

3, 11, 61, 457, 5237, 1226677, 34543329507310391, 1636619248175258407, 5186576044693944076609, 742779051038516950393163206833793, 1506853388294906471801157206440769816406928024502711, 651879075122842895567706351814676957742356330143458665568047

Offset

1,1

Comments

Primes which are the sum of the numerator and the denominator of partial sums of the reciprocals of primes.

Each term of this sequence can be expressed as the sum of an expression with exactly one odd term and n even terms, where the odd term is A002110(n)/A002110(1), and n > 0 (see Alexander Adamchuk comment in A024528).

a(2) = 11 = 3 + 2 + 6 contains the only prime odd term 3.

Links

Table of n, a(n) for n=1..12.

Example

3 is a term because 1/2 = 1/2 and 1 + 2 = 3 which is prime.
11 is a term because 1/2 + 1/3 = 5/6 and 5 + 6 = 11 which is prime.
61 is a term because 5/6 + 1/5 = 31/30 and 31 + 30 = 61 which is prime.
457 is a term because 31/30 + 1/7 = 247/210 and 247 + 210 = 457 which is prime.

Crossrefs

Intersection of A000040 and A024528.

Cf. A002110.

Sequence in context: A095237 A185385 A024528 * A273468 A004108 A203007

Adjacent sequences: A368877 A368878 A368879 * A368881 A368882 A368883

Keyword

nonn

Author

Torlach Rush, Jan 08 2024

Status

approved