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A373124
Sum of indices of primes between powers of 2.
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).
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
Sequence in context: A106013 A175445 A352762 * A073623 A101592 A349709
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 31 2024
STATUS
approved