A373124 Sum of indices of primes between powers of 2.

1, 2, 7, 11, 45, 105, 325, 989, 3268, 10125, 33017, 111435, 369576, 1277044, 4362878, 15233325, 53647473, 189461874, 676856245, 2422723580, 8743378141, 31684991912, 115347765988, 421763257890, 1548503690949, 5702720842940, 21074884894536, 78123777847065

Offset: 0

Author

Gus Wiseman, May 31 2024

Keywords

• nonn

Comments

Sum of k such that 2^n+1 <= prime(k) <= 2^(n+1).

Examples

			Row-sums of the sequence of all positive integers as a triangle with row-lengths A036378:
   1
   2
   3  4
   5  6
   7  8  9 10 11
  12 13 14 15 16 17 18
  19 20 21 22 23 24 25 26 27 28 29 30 31
  32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
		

Crossrefs

For indices of primes between powers of 2:

- sum A373124 (this sequence)

- length A036378

- min A372684 (except initial terms), delta A092131

- max A007053

For primes between powers of 2:

- sum A293697

- length A036378

- min A104080 or A014210

- max A014234, delta A013603

For squarefree numbers between powers of 2:

- sum A373123

- length A077643, run-lengths of A372475

- min A372683, delta A373125, indices A372540

- max A372889, delta A373126, indices A143658

Cf. A000040, A000120, A014499, A029837, A029931, A035100, A069010, A070939, A112925, A112926, A211997.

Programs

Mathematica

Table[Total[PrimePi/@Select[Range[2^(n-1)+1,2^n],PrimeQ]],{n,10}]

PARI

ip(n) = primepi(1<A007053
t(n) = n*(n+1)/2; \\ A000217
a(n) = t(ip(n+1)) - t(ip(n)); \\ Michel Marcus, May 31 2024