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

1,1

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

Links

Table of n, a(n) for n=1..32.

Example

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.

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);

Prog

(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<<i) + 1), listput(res, (j<<i) + 1) ) ) ); Set(res) } \\ David A. Corneth, Mar 03 2023

Crossrefs

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

Cf. A057023, A023506.

Sequence in context: A100003 A283331 A114161 * A372867 A302199 A346791

Adjacent sequences: A361177 A361178 A361179 * A361181 A361182 A361183

Keyword

nonn

Author

Lorenzo Sauras Altuzarra, Mar 03 2023

Extensions

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

More terms from David A. Corneth, Mar 03 2023

Status

approved