A086477
Primes p such that 128p+1 and (p-1)/128 are both prime.
Original entry on oeis.org
21377, 44417, 140417, 151169, 151937, 155777, 436097, 539009, 569729, 570497, 608129, 658817, 704897, 830849, 865409, 965249, 1000577, 1008257, 1054337, 1130369, 1214849, 1311617, 1419137, 1429889, 1556609, 1618817, 1779329
Offset: 1
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Prime[ Select[ Range[141120], PrimeQ[(Prime[ # ] - 1)/2^7] && PrimeQ[2^7Prime[ # ] + 1] & ]]
Select[Prime[Range[140000]],AllTrue[{128#+1,(#-1)/128},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 13 2019 *)
A086478
Primes p such that 512p+1 and (p-1)/512 are both prime.
Original entry on oeis.org
183809, 220673, 420353, 629249, 696833, 1772033, 1904129, 2186753, 4137473, 4930049, 5575169, 6435329, 7040513, 8355329, 9405953, 9491969, 9882113, 10112513, 10373633, 11580929, 11648513, 11725313, 13209089, 13445633
Offset: 1
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Prime[ Select[ Range[957580], PrimeQ[(Prime[ # ] - 1)/512] && PrimeQ[512Prime[ # ] + 1] &]]
Select[Prime[Range[900000]],AllTrue[{512#+1,(#-1)/512},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 13 2018 *)
A085832
Smallest prime p such that both (p-1)/2^(2n-1) and 2^(2n-1)*p+1 are primes.
Original entry on oeis.org
5, 17, 1889, 21377, 183809, 83969, 40961, 79003649, 245235713, 5767169, 1004535809, 897581057, 41238396929, 13555990529, 2357400174593, 3438121320449, 12360915877889, 188188287041537, 286010462175233
Offset: 1
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f[n_] := Block[{k = 1}, While[ !PrimeQ[k] || !PrimeQ[(k - 1)/2^n] || !PrimeQ[2^n*k + 1], k += 2^n]; k]; Table[ f[n], {n, 1, 37, 2}]
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