A206581 Odd primes p such that p+1 is a prime times a power of two.

5, 11, 13, 19, 23, 37, 43, 47, 61, 67, 73, 79, 103, 151, 157, 163, 191, 193, 211, 223, 271, 277, 283, 313, 331, 367, 383, 397, 421, 457, 463, 487, 523, 541, 547, 607, 613, 631, 661, 673, 691, 733, 751, 757, 787, 823, 877, 907, 991, 997, 1051, 1087, 1093

Offset: 1

Author

T. D. Noe, Mar 07 2012

Keywords

• nonn

Comments

Very similar to A192869; here p+1 = q*2^k, where q must be prime.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Kevin Broughan and Zhou Qizhi, Flat primes and thin primes, Bulletin of the Australian Mathematical Society 82:2 (2010), pp. 282-292.

Crossrefs

Subsequence of A192869.

Programs

Mathematica

Select[Prime[Range[2, 1000]], PrimeQ[(#+1)/2^IntegerExponent[#+1, 2]] &]

PARI

is(n)=isprime(n) && n>4 && isprime((n+1)>>valuation(n+1,2)) \\ Charles R Greathouse IV, Sep 15 2015

Formula

a(n) >> n log^2 n is implicit in Broughan & Qizhi, see A192869. - Charles R Greathouse IV, Sep 15 2015