A101795 Primes of the form 4*k-1 such that 8*k-1, 16*k-1 and 32*k-1 are also primes.

179, 359, 2699, 3539, 12119, 17159, 27479, 53639, 57839, 63419, 71399, 74699, 82499, 87539, 101399, 107279, 107699, 112919, 122099, 122819, 126839, 127139, 133499, 139439, 166739, 167759, 229739, 253679, 254279, 287219, 296099

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

a(n) = 4*A101794(n) - 1. - Amiram Eldar, May 13 2024

Example

4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719 and 32*45-1 = 1439 are primes, so 179 is a term.

Mathematica

Select[Table[4n-1, {n, 75000}], AllTrue[(#+1)*{1, 2, 4, 8}-1, PrimeQ]&] (* Harvey P. Dale, Apr 23 2019 *)

Prog

(PARI) is(k) = if(k % 4 == 3, my(m = k\4 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1), 0); \\ Amiram Eldar, May 13 2024

Crossrefs

Cf. A002515, A101794, A101796, A101797, A101798.

Subsequence of A002145 and A101791.

Subsequence: A101995.

Sequence in context: A142670 A142948 A109985 * A142389 A063350 A094492

Adjacent sequences: A101792 A101793 A101794 * A101796 A101797 A101798

Keyword

easy,nonn

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004

Status

approved