A095297
Number of A095287-primes in range ]2^n,2^(n+1)].
Original entry on oeis.org
0, 1, 0, 2, 2, 8, 7, 22, 27, 68, 80, 235, 343, 844, 1180, 2849, 4473, 10138, 15387, 37023, 58714, 134477, 213397, 494625, 802311, 1829183, 2965114, 6789809, 11185644, 25412867, 42048314, 95440507, 159433693
Offset: 1
A095334
Number of A095314-primes in range ]2^n,2^(n+1)].
Original entry on oeis.org
0, 1, 0, 3, 3, 5, 4, 21, 32, 69, 96, 229, 335, 768, 1116, 2860, 4371, 10252, 15490, 36563, 58041, 133739, 209875, 491193, 795599, 1816561, 2951789, 6772098, 11144763, 25284670, 41781268, 94895078, 158643268
Offset: 1
A095742
Sum of A037888(p) for all primes p such that 2^n < p < 2^(n+1).
Original entry on oeis.org
0, 0, 2, 3, 9, 16, 35, 69, 148, 271, 628, 1167, 2629, 4830, 10597, 20083, 42928, 81579, 174223, 331314, 701382, 1340756, 2825575, 5422454, 11361615, 21873923, 45673361, 88161666, 183458213, 354899159, 736343490, 1427495050, 2954560104
Offset: 1
a(1)=0, as only prime in range ]2,4] is 3, which has palindromic binary expansion 11, i.e. A037888(3)=0. a(2)=0, as in range ]4,8] there are two primes 5 (101 in binary) and 7 (111 in binary) so A037888(5) + A037888(7) = 0. a(3)=2, as in range ]8,16] there are two primes, 11 (1011 in binary) and 13 (1101 in binary), thus A037888(11) + A037888(13) = 1+1 = 2.
A095296
Number of A095286-primes in range ]2^n,2^(n+1)].
Original entry on oeis.org
1, 1, 2, 3, 5, 5, 16, 21, 48, 69, 175, 229, 529, 768, 1850, 2860, 6276, 10252, 23248, 36563, 81622, 133739, 300311, 491193, 1091809, 1816561, 4062176, 6772098, 15021634, 25284670, 56134342, 94895078, 209889612
Offset: 1
A095353
Sum of 1-fibits in Zeckendorf-expansion A014417(p) summed for all primes p in range [Fib(n+1),Fib(n+2)[ (where Fib = A000045).
Original entry on oeis.org
0, 1, 1, 3, 2, 7, 7, 14, 23, 35, 56, 94, 155, 243, 402, 614, 1061, 1656, 2689, 4295, 6938, 11176, 18095, 29102, 46907, 75703, 122174, 197494, 317987, 514611, 829595, 1340861, 2166008, 3497040, 5645418, 9120129, 14733126, 23803219, 38460014
Offset: 1
a(1) = a(2) = 0, as there are no primes in ranges [1,2[ and [2,3[. a(3)=1 as in [3,5[ there is prime 3 with Fibonacci-representation 100. a(4)=3, as in [5,8[ there are primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively and we have three 1-fibits in total. a(5)=2, as in [8,13[ there is only one prime 11, with Zeckendorf-representation 10100.
Cf.
A095336,
A095298 (similar sums and ratios computed in binary system).
A095765
Number of primes in range [2^n+1, 2^(n+1)] whose binary expansion begins '10' (A080165).
Original entry on oeis.org
0, 1, 1, 3, 4, 6, 12, 22, 38, 70, 130, 237, 441, 825, 1539, 2897, 5453, 10335, 19556, 37243, 70938, 135555, 259586, 497790, 956126, 1839597, 3544827, 6839282, 13212389, 25552386, 49472951, 95883938, 186011076, 361177503, 701906519
Offset: 1
Table showing the derivation of the initial terms:
n 2^n+1 2^(n+1) a(n) primes starting '10' in binary
1 3 4 0 -
2 5 8 1 5 = 101_2
3 9 16 1 11 = 1011_2
4 17 32 3 17 = 10001_2, 19 = 10011_2, 23 = 10111_2
Edited, restoring meaning of name, by
Peter Munn, Jun 27 2023
A095336
Sum of 1-fibits in Zeckendorf-expansion A014417(p) summed for all primes p in range ]2^n,2^(n+1)].
Original entry on oeis.org
1, 3, 3, 13, 20, 41, 76, 176, 325, 638, 1353, 2533, 5223, 10186, 20504, 40775, 80661, 163765, 318602, 649948, 1268922, 2571531, 5082895, 10217300, 20327307, 40399966, 82164918, 160343669, 324931245, 640501167, 1290990369, 2567150515
Offset: 1
a(1)=1, as only prime in range ]2,4] is 3, whose Fibonacci-representation is 100. In the next range we have primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively, thus a(2)=3.
Showing 1-7 of 7 results.
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