A266233 -id:A266233 - cp's OEIS frontend

A266234 Primes representable as f(f(f(...f(p)...))) where p is a prime and f(x) = x*2 - 1.

3, 5, 13, 17, 37, 41, 61, 73, 89, 97, 113, 157, 193, 233, 241, 257, 277, 281, 313, 337, 353, 397, 401, 409, 421, 433, 449, 457, 521, 541, 577, 593, 601, 613, 641, 661, 673, 733, 757, 761, 769, 877, 929, 953, 997, 1009, 1049, 1093, 1129, 1153, 1201, 1213, 1237

Offset: 1

Alex Ratushnyak, Dec 25 2015

nonn

A005383 is a subsequence: f(x) is applied just once.

Cf. A000040, A005383, A266233.

Take[Union@ Flatten[Table[Nest[2 # - 1 &, Prime@ n, #], {n, 120}] & /@ Range@ 120] /. n_ /; CompositeQ@ n -> Nothing, 53] (* Michael De Vlieger, Jan 06 2016 *)

A266235 Primes representable as f(f(f(...f(p)...))) where p is a prime and f(x) = x^2 + 1.

Original entry on oeis.org

5, 101, 677, 28901, 3422501, 4884101, 260176901, 4784488901, 5887492901, 7370222501, 12898144901, 14498568101, 24840912101, 38514062501, 47563248101, 56249608901, 64014060101, 110842384901, 123657722501, 135755402501, 205145584901, 279343960901, 288680544101

Offset: 1

Alex Ratushnyak, Dec 25 2015

nonn

For p>2, f(x) is applied an even number of times, twice at least.

			a(2) = f(f(3)) = (3^2 + 1)^2 + 1 = 101.
a(3) = f(f(5)) = (5^2 + 1)^2 + 1 = 677.

Cf. A000040, A266233.

Take[Union@ Flatten[Table[Nest[#^2 + 1 &, Prime@ n, #], {n, 150}] & /@ Range@ 6] /. n_ /; CompositeQ@ n -> Nothing, 23] (* Michael De Vlieger, Jan 06 2016 *)

from sympy import isprime
a=[]
TOP=1000000
for p in range(TOP):
    if isprime(p):
        q=p
        while q

A274589 Primes not of the form (prime+1)*2^k-1 with k>=1.

Original entry on oeis.org

2, 3, 13, 17, 19, 29, 37, 41, 43, 53, 61, 67, 73, 89, 97, 101, 103, 109, 113, 131, 137, 139, 149, 157, 163, 173, 181, 193, 197, 199, 211, 229, 233, 241, 251, 257, 269, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 349, 353, 367

Offset: 1

Gionata Neri, Jun 29 2016

nonn

A permutation of A057026 (excluding the zeros, e.g., A057026(254601) = 0).

			103 = (51+1)*2^1-1 = (25+1)*2^2-1 = (12+1)*2^3-1, the numbers 51, 25 and 12 are not primes, so 103 is in the sequence.
71 = (35+1)*2^1-1 = (17+1)*2^2-1 = (8+1)*2^3-1, the number 17 is prime, so 71 is not in the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A057026, A266233 (complement with respect to A000040).

filter := proc(n) local k;
  if not isprime(n) then return false fi;
  for k from 1 to padic:-ordp(n+1,2) do
     if isprime((n+1)/2^k-1) then return false
     fi
  od:
  true
end proc:
select(filter, [2,seq(i,i=3..1000,2)]); # Robert Israel, Jun 29 2016

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A266234 Primes representable as f(f(f(...f(p)...))) where p is a prime and f(x) = x*2 - 1.

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A266235 Primes representable as f(f(f(...f(p)...))) where p is a prime and f(x) = x^2 + 1.

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A274589 Primes not of the form (prime+1)*2^k-1 with k>=1.

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