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A140126 Partial sums of A001912. 1

%I #8 Jan 29 2017 11:00:28

%S 1,3,6,11,18,26,36,48,61,79,99,126,154,187,224,266,311,358,413,471,

%T 531,593,656,721,788,861,936,1014,1094,1179,1267,1357,1449,1551,1654,

%U 1759,1871,1986,2104,2224,2349,2477,2607,2739,2874,3014,3156,3306,3459,3616

%N Partial sums of A001912.

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

%e 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.

%p 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

%t Accumulate[Select[Range[200],PrimeQ[4#^2+1]&]] (* _Harvey P. Dale_, Jan 29 2017 *)

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

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Jun 04 2008

%E More terms from _R. J. Mathar_, Jun 12 2008

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)