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

2, 3, 12, 41, 139, 442, 1349, 4093, 12108, 35153, 101295, 289048, 819477, 2309689, 6472406, 18054351, 50153807, 138847614, 383282511, 1054875523, 2895955030, 7931352725, 21678032713, 59142462326, 161068803147, 437935857313, 1188967702870, 3223626641605, 8729120815845, 23609318259832

Offset: 1

Author

Harish Chalwadi, May 24 2024

Keywords

• nonn

Examples

			The primes and the groups of them summed begin
  primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...
         \/ \/ \--/  \--------/  \----------------/
  F(n) =  1, 1,  2,      3,               5,      group length
  a(n) =  2, 3, 12,     41,             139,      group sum
a(1) = 2 because the first f(1)=1 prime is 2.
a(2) = 3 because the next f(2)=1 prime is 3.
a(3) = 12 because the next f(2)=2 primes are 5 and 7 which add up to 12.
a(4) = 41 because the next f(3)=3 primes are 11, 13 and 17, and they add up to 41.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..49

Crossrefs

Cf. A000040, A000045, A000071, A007504, A034958, A105554.

Programs

Mathematica

With[{m = 30}, Plus @@@ TakeList[Prime[Range[Fibonacci[m + 2] - 1]], Fibonacci[Range[m]]]] (* Amiram Eldar, May 25 2024 *)

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, ", "))};
a371877(30) \\ Hugo Pfoertner, May 25 2024

Extensions

a(11)-a(23) from Michel Marcus, May 25 2024

a(24)-a(30) from Hugo Pfoertner, May 25 2024