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
Examples
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) ...
Links
- Michel Marcus, Table of n, a(n) for n = 1..8217
Programs
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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
Extensions
Name corrected by Jon E. Schoenfield, Jun 27 2021
More terms from Michel Marcus, Jan 22 2022
Comments