A072742 Lesser members of a pair of primes (p, q) such that, for some integer k, (p+q)/2 = 2^k and p > 2^(k-1).

3, 5, 13, 17, 23, 61, 83, 89, 107, 139, 163, 181, 199, 229, 241, 263, 281, 347, 383, 431, 461, 467, 503, 577, 601, 619, 727, 751, 757, 769, 811, 877, 919, 997, 1009, 1097, 1187, 1193, 1217, 1259, 1277, 1307, 1319, 1367, 1409, 1433, 1439, 1487, 1553, 1619, 1637, 1697, 1787, 1823, 1889, 1997, 2027

Offset

1,1

Comments

For each term p=a(n), the corresponding greater member is q=A072743(n).

Links

Michel Marcus, Table of n, a(n) for n = 1..8217

Example

   n  p = a(n)  q = A072743(n)   (p+q)/2
  --  --------  --------------  ---------
   1      3            5          4 = 2^2
   2      5           11          8 = 2^3
   3     13           19         16 = 2^4
   4     17           47         32 = 2^5
   5     23           41         32 = 2^5
   6     61           67         64 = 2^6
   7     83          173        128 = 2^7
   8     89          167        128 = 2^7
   9    107          149        128 = 2^7
  10    139          373        256 = 2^8
As an irregular triangle, sequence begins:
  [3],                             (k=2)
  [5],                             (k=3)
  [13],                            (k=4)
  [17, 23],                        (k=5)
  [61],                            (k=6)
  [83, 89, 107],                   (k=7)
  [139, 163, 181, 199, 229, 241],  (k=8)
  ...

Prog

(PARI) listk(k) = {my(list = List()); forprime(p=2^(k-1)+1, 2^k, my(q=2^(k+1)-p); if ((q>p) && isprime(q), listput(list, p)); ); Vec(list); }
upto(k) = {my(list = List()); for (i=1, k, my(klist = listk(i)); if (#klist, for (j=1, #klist, listput(list, klist[j]))); ); Vec(list); }
upto(11) \\ Michel Marcus, Jan 22 2022

Crossrefs

Cf. A072743, A072744, A072745, A072746.

Sequence in context: A105900 A260191 A094745 * A076189 A291282 A073654

Adjacent sequences: A072739 A072740 A072741 * A072743 A072744 A072745

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Jul 08 2002

Extensions

Name corrected by Jon E. Schoenfield, Jun 27 2021

More terms from Michel Marcus, Jan 22 2022

Status

approved