A168156 Sum of the binary digits of all primes between 2^(n-1) and 2^n-1, i.e., with exactly n binary digits.
0, 3, 5, 6, 18, 29, 56, 113, 240, 452, 885, 1790, 3474, 6951, 13671, 27183, 54201, 107224, 213882, 424513, 845716, 1682456, 3350362, 6671581, 13299828, 26500297, 52829961, 105342821, 210088965, 419106389, 836097752, 1668341390, 3329412989, 6645128078
Offset: 1
Examples
No prime can be written with only 1 binary digit, thus a(1)=0. The primes that can be written with 2 binary digits are 2 = 10[2] and 3 = 11[2], they have 3 nonzero bits, so a(2)=3. Primes with 3 binary digits are 5 = 101[2] and 7 = 111[3]. They have a total of a(3)=5 nonzero bits.
Crossrefs
Cf. A086904.
Programs
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PARI
s=0; L=p=2; while( L*=2, print1(s", "); s=0; until( L
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PARI
a(n)=my(s); forprime(p=2^(n-1),2^n-1, s+=hammingweight(p)); s \\ Charles R Greathouse IV, Apr 07 2020
Extensions
a(26)-a(32) from Donovan Johnson, Jul 28 2010
a(33) from Chai Wah Wu, Apr 06 2020
a(34) from Chai Wah Wu, Apr 07 2020
Comments