A361180 Primes p such that the odd part of p - 1 is upper-bounded by the dyadic valuation of p - 1.

3, 5, 17, 97, 193, 257, 641, 769, 12289, 18433, 40961, 65537, 114689, 147457, 163841, 786433, 1179649, 5767169, 7340033, 13631489, 23068673, 167772161, 469762049, 2013265921, 2281701377, 3221225473, 3489660929, 12348030977, 77309411329, 206158430209, 2061584302081, 2748779069441

Offset: 1

Author

Lorenzo Sauras Altuzarra, Mar 03 2023

Keywords

• nonn

Comments

Primes of the form k*2^m + 1 where k <= m and k is odd. - David A. Corneth, Mar 03 2023

Primes prime(k) such that A057023(k) <= A023506(k). - Michel Marcus, Mar 09 2023

Examples

			3 is a term because the odd part of 2 is 1, the dyadic valuation of 2 is 1 and 1 <= 1.
641 = 5*2^7 + 1 is a term because the odd part of 640 is 5, the dyadic valuation of 640 is 7 and 5 <= 7.
		

Crossrefs

Cf. A000040 (primes), A000265 (odd part), A007814 (dyadic valuation).

Cf. A057023, A023506.

Programs

Maple

# Maple program due to David A. Corneth, Mar 03 2023
aList := proc(upto)
   local i, j, p, R:
   R := {}:
   for i from 1 to ilog2(upto) do
      for j from 1 to min(i, floor(upto/2^i)) do
         p := j*2^i+1:
         if isprime(p) then R := `union`(R, {p}): fi: od: od:
   R: end:
aList(10^12);

PARI

isok(p) = if (isprime(p), my(m=valuation(p-1,2)); (p-1)/2^m <= m); \\ Michel Marcus, Mar 03 2023

PARI

upto(n) = {my(res = List()); for(i = 1, logint(n, 2), forstep(j = 1, min(i, n>>i), 2, if(isprime((j<David A. Corneth, Mar 03 2023

Extensions

a(17)..a(27) from Michel Marcus, Mar 03 2023

More terms from David A. Corneth, Mar 03 2023