A215050
Number of primes of the form 1 + b^16 for 1 < b < 10^n.
Original entry on oeis.org
1, 5, 48, 291, 2194, 17907, 152447, 1322985, 11669082
Offset: 1
a(1) = 1 because the only Fermat prime F_4(b) where b<10^1 is the prime 65537.
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Table[Length[Select[Range[2,10^n-1]^16 + 1, PrimeQ]], {n, 5}] (* T. D. Noe, Aug 02 2012 *)
Module[{nn=8,t},t=Table[If[PrimeQ[n^16+1],1,0],{n,2,10^nn}];Table[Total[ Take[t,10^i-1]],{i,nn}]] (* Harvey P. Dale, Sep 14 2015 *)
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a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^16+1))
A215057
Number of primes of the form 1 + b^64 for 1 < b < 10^n.
Original entry on oeis.org
0, 0, 8, 92, 606, 4835, 41059, 354239, 3133668
Offset: 1
a(3) = 8 because the Fermat numbers F_6(b) where b<10^3 are prime only for b = 102, 162, 274, 300, 412, 562, 592, 728.
A215058
Number of primes of the form 1 + b^128 for 1 < b < 10^n.
Original entry on oeis.org
0, 0, 7, 25, 242, 1933, 16080, 139921, 1234958
Offset: 1
a(3) = 7 because the generalized Fermat numbers F_7(b) where b<10^3 are prime only for b: 120, 190, 234, 506, 532, 548, 960.
A215698
Number of primes of the form 1 + b^256 for 1 < b < 10^n.
Original entry on oeis.org
0, 0, 4, 30, 272, 2322
Offset: 1
a(3) = 4 because the generalized Fermat numbers F_8(b) where b<10^3 are prime only for b: 278, 614, 892, 898.
A215699
Number of primes of the form 1 + b^512 for 1 < b < 10^n.
Original entry on oeis.org
0, 1, 1, 28, 160, 1247
Offset: 1
a(3) = 1 because the generalized Fermat numbers F_9(b) where b<10^3 are prime only for b = 46.
A215700
Number of primes of the form 1 + b^1024 for 1 < b < 10^n.
Original entry on oeis.org
0, 0, 1, 14, 81, 578
Offset: 1
a(3) = 1 because the generalized Fermat numbers F_10(b) where b<10^3 are prime only for b = 824.
A215701
Number of primes of the form 1 + b^2048 for 1 < b < 10^n.
Original entry on oeis.org
0, 0, 1, 4, 40, 276
Offset: 1
a(4) = 4 because the generalized Fermat numbers F_11(b) where b<10^4 are prime only for b = 150, 2558, 4650, 4772.
A215702
Number of primes of the form 1 + b^4096 for 1 < b < 10^n.
Original entry on oeis.org
0, 0, 0, 2, 16, 170
Offset: 1
a(4) = 2 because the generalized Fermat numbers F_12(b) where b<10^4 are prime only for b = 1534, 7316.
A215961
Number of primes of the form 1 + b^8192 for 1 < b < 10^n.
Original entry on oeis.org
0, 0, 0, 0, 3, 74, 621
Offset: 1
a(5) = 3 because the generalized Fermat numbers F_13(b) where b<10^5 are prime only for b = 30406, 71852, 85654.
A215962
Number of primes of the form 1 + b^16384 for 1 < b < 10^n.
Original entry on oeis.org
0, 0, 0, 0, 1, 33, 137
Offset: 1
a(5) = 1 because the generalized Fermat numbers F_14(b) where b<10^5 are prime only for b = 67234.
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