A072746 -id:A072746 - cp's OEIS frontend

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

Reinhard Zumkeller, Jul 08 2002

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

			   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)
  ...

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

Cf. A072743, A072744, A072745, A072746.

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

Name corrected by Jon E. Schoenfield, Jun 27 2021

More terms from Michel Marcus, Jan 22 2022

A072743 Greater members of a pair of primes (p, q) such that, for some integer k, (p+q)/2 = 2^k and p > 2^(k-1).

Original entry on oeis.org

5, 11, 19, 47, 41, 67, 173, 167, 149, 373, 349, 331, 313, 283, 271, 761, 743, 677, 641, 593, 563, 557, 521, 1471, 1447, 1429, 1321, 1297, 1291, 1279, 1237, 1171, 1129, 1051, 1039, 2999, 2909, 2903, 2879, 2837, 2819, 2789, 2777, 2729, 2687, 2663, 2657

Offset: 1

Reinhard Zumkeller, Jul 08 2002

nonn

For each term q=a(n), the corresponding lesser member is p=A072742(n). (Terms in this sequence are not listed in ascending order; rather, the corresponding primes p in A072742 are listed in ascending order.)

Cf. A072742 (corresponding lesser members), A072746, A072744, A072745.

listkq(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, q)); ); Vec(list);}
upto(k) = {my(list = List()); for (i=1, k, my(klist = listkq(i)); if (#klist, for (j=1, #klist, listput(list, klist[j])));); Vec(list);}
upto(11) \\ Michel Marcus, Jan 22 2022

Name corrected by Jon E. Schoenfield, Jun 30 2021

cp's OEIS Frontend

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).

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