A158035 2 * A158034 + 1, prime numbers p for which f = (2^p - 2^((p - 1) / 2 + 1) + 4p^2 - 8p) / (2p^2 - 2p) is an integer.

7, 23, 47, 167, 263, 359, 383, 479, 487, 503, 719, 839, 863, 887, 983, 1319, 1367, 1439, 1487, 1783, 1823, 2039, 2063, 2207, 2447, 2879, 2903, 2999, 3023, 3079, 3119, 3167, 3623, 3863, 4007, 4079, 4127, 4423, 4679, 4703, 4799, 4919, 5023, 5087, 5399, 5639

Offset

1,1

Comments

(p - 1) / 2 is often prime.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Maple

A158035 := proc(n) local i, am, p, tren;
am := [ ]:
for i from 2 to n do
  p := ithprime(i):
  tren := (2^(p) - 2^((p - 1) / 2 + 1) + 4*p^(2) - 8*p) / (2*p^(2) - 2*p):
  if (type( tren, 'integer') = 'true') then
    am := [op(am), p]:
  fi
od; RETURN(am) end:
A158035(740); # Jani Melik, May 06 2013

Mathematica

Select[Prime[Range[800]], IntegerQ[(2^#-2^((#-1)/2+1)+4#^2-8#)/(2#^2-2#)]&] (* Harvey P. Dale, Nov 08 2017 *)

Crossrefs

Cf. A158034.

Cf. A002515 (Lucasian primes).

Cf. A145918 (exponential Sophie Germain primes).

Cf. A046318, A139876 (related to composite members of A158034: 243, 891, 1539, and 2511).

Sequence in context: A139830 A153210 A185955 * A101789 A174590 A162290

Adjacent sequences: A158032 A158033 A158034 * A158036 A158037 A158038

Keyword

easy,nonn

Author

Reikku Kulon, Mar 11 2009

Status

approved