A262392 a(n) = A007504(n) + A010693(n).

2, 5, 7, 13, 19, 31, 43, 61, 79, 103, 131, 163, 199, 241, 283, 331, 383, 443, 503, 571, 641, 715, 793, 877, 965, 1063, 1163, 1267, 1373, 1483, 1595, 1723, 1853, 1991, 2129, 2279, 2429, 2587, 2749, 2917, 3089, 3269, 3449, 3641, 3833, 4031, 4229

Offset

0,1

Comments

Sequence is interesting because of the fact that a(n) is a prime number for n = 0..20.

Main inspiration of sequence was indices of prime numbers in A036439 and A227547.

Links

Table of n, a(n) for n=0..46.

Formula

a(n) = Sum_{k=1..n} prime(k) + n mod 2 + 2 for n>0, a(0)=2 (from Pari code).

Example

a(0) = A007504(0) + A010693(0) = 0 + 2 = 2.
a(1) = A007504(1) + A010693(1) = 2 + 3 = 5.
a(2) = A007504(2) + A010693(2) = 5 + 2 = 7.
a(3) = A007504(3) + A010693(3) = 10 + 3 = 13.
a(4) = A007504(4) + A010693(4) = 17 + 2 = 19.
a(5) = A007504(5) + A010693(5) = 28 + 3 = 31.

Mathematica

s = Accumulate@ Prime@ Range@ 1200; {2}~Join~Table[s[[n]] + If[OddQ@ n, 3, 2], {n, 46}] (* Michael De Vlieger, Sep 21 2015 *)

Prog

(PARI) a(n) = sum(k=1, n, prime(k)) + (n%2) + 2;
vector(50, n, a(n-1))

Crossrefs

Cf. A036439, A227547, A007504, A010693, A071148.

Sequence in context: A275011 A094743 A175075 * A056985 A082182 A032719

Adjacent sequences: A262389 A262390 A262391 * A262393 A262394 A262395

Keyword

nonn,easy

Author

Altug Alkan, Sep 21 2015

Status

approved