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A371877 Divide primes into groups with Fibonacci(n) elements and add together.

%I A371877 #41 Jun 16 2024 05:10:14
%S A371877 2,3,12,41,139,442,1349,4093,12108,35153,101295,289048,819477,2309689,
%T A371877 6472406,18054351,50153807,138847614,383282511,1054875523,2895955030,
%U A371877 7931352725,21678032713,59142462326,161068803147,437935857313,1188967702870,3223626641605,8729120815845,23609318259832
%N A371877 Divide primes into groups with Fibonacci(n) elements and add together.
%H A371877 Hugo Pfoertner, <a href="/A371877/b371877.txt">Table of n, a(n) for n = 1..49</a>
%e A371877 The primes and the groups of them summed begin
%e A371877   primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...
%e A371877          \/ \/ \--/  \--------/  \----------------/
%e A371877   F(n) =  1, 1,  2,      3,               5,      group length
%e A371877   a(n) =  2, 3, 12,     41,             139,      group sum
%e A371877 a(1) = 2 because the first f(1)=1 prime is 2.
%e A371877 a(2) = 3 because the next f(2)=1 prime is 3.
%e A371877 a(3) = 12 because the next f(2)=2 primes are 5 and 7 which add up to 12.
%e A371877 a(4) = 41 because the next f(3)=3 primes are 11, 13 and 17, and they add up to 41.
%t A371877 With[{m = 30}, Plus @@@ TakeList[Prime[Range[Fibonacci[m + 2] - 1]], Fibonacci[Range[m]]]] (* _Amiram Eldar_, May 25 2024 *)
%o A371877 (PARI) a371877(nterms) = {my (n1=0, n2=1, p=1); for (n=1, nterms, n1=n2; n2=n1+fibonacci(n); my(s=0); for(k=n1, n2-1, s+=p=nextprime(p+1)); print1 (s, ", "))};
%o A371877 a371877(30) \\ _Hugo Pfoertner_, May 25 2024
%Y A371877 Cf. A000040, A000045, A000071, A007504, A034958, A105554.
%K A371877 nonn
%O A371877 1,1
%A A371877 _Harish Chalwadi_, May 24 2024
%E A371877 a(11)-a(23) from _Michel Marcus_, May 25 2024
%E A371877 a(24)-a(30) from _Hugo Pfoertner_, May 25 2024