A140126 Partial sums of A001912.

1, 3, 6, 11, 18, 26, 36, 48, 61, 79, 99, 126, 154, 187, 224, 266, 311, 358, 413, 471, 531, 593, 656, 721, 788, 861, 936, 1014, 1094, 1179, 1267, 1357, 1449, 1551, 1654, 1759, 1871, 1986, 2104, 2224, 2349, 2477, 2607, 2739, 2874, 3014, 3156, 3306, 3459, 3616

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = SUM[i=1..n] A001912(i) = SUM[j=1..n] {Numbers i_j such that 4*(i_j)^2 + 1 is prime}.

Example

a(17) = 1 + 2 + 3 + 5 + 7 + 8 + 10 + 12 + 13 + 18 + 20 + 27 + 28 + 33 + 37 + 42 + 45 = 311 which is itself a prime. The primes in this sequence begin: 3, 11, 61, 79, 311, 593.

Maple

A001912 := proc(n) option remember ; local a ; if n <= 3 then RETURN(n); else for a from A001912(n-1)+1 do if isprime(4*a^2+1) then RETURN(a) ; fi ; od: fi ; end: A140126 := proc(n) local i ; add( A001912(i), i=1..n) ; end: seq(A140126(n), n=1..80) ; # R. J. Mathar, Jun 12 2008

Mathematica

Accumulate[Select[Range[200], PrimeQ[4#^2+1]&]] (* Harvey P. Dale, Jan 29 2017 *)

Crossrefs

Cf. A000040, A001912, A002496, A005574, A062325, A090693.

Sequence in context: A363056 A025210 A340648 * A140235 A224214 A010000

Adjacent sequences: A140123 A140124 A140125 * A140127 A140128 A140129

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 04 2008

Extensions

More terms from R. J. Mathar, Jun 12 2008

Status

approved