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

0,2

Comments

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

Links

Table of n, a(n) for n=0..27.

Example

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

Mathematica

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

Prog

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

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.

Sequence in context: A106013 A175445 A352762 * A073623 A101592 A349709

Adjacent sequences: A373121 A373122 A373123 * A373125 A373126 A373127

Keyword

nonn

Author

Gus Wiseman, May 31 2024

Status

approved