|
| |
|
|
A358571
|
|
Lesser p of a sexy prime pair such that (p-3)/2 is also the lesser prime of a sexy prime pair.
|
|
1
|
|
|
|
13, 17, 37, 97, 457, 557, 1117, 1217, 1297, 2237, 2377, 2897, 4937, 7237, 9277, 10457, 18797, 21317, 23557, 24077, 27817, 29437, 30757, 34757, 38917, 39157, 48157, 48817, 50497, 55897, 60617, 62297, 64997, 72617, 81157, 82457, 90017, 94597, 107837, 108877, 111857
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Equivalently, sums of the form (sexy primes - 3) which are also the lesser prime of a sexy prime pair.
Also numbers m such that m-4, m-1, m+5 and m+8 cannot be represented as x*y + x + y, with x >= y > 1 (A254636).
More generally, any sequence of numbers m such that A254636(m - 2*k - 2), A254636(m - 1), A254636(m + 4*k + 1) and A254636(m + 6*k + 2) are all 0 will only provide prime numbers which are lesser of a pair of primes (p, q) such that the pair (r, s) forms also a pair of primes, where q = p + 2*(2*k + 1), r = (p - 2*k - 1)/2, and s = (q + 2*k + 1)/2. Obviously, s - r = q - p = 2*(2*k + 1).
For k = 0, we get sequence A256386 (starting from its 6th term).
For k = 1, this sequence.
For k = 2, sequence starts: 19, 31, 43, 79, 127, 163, 283, 547, 751, 919, ...
For k = 3, sequence starts: 17, 53, 113, 593, 773, 1553, 1733, 1973, 4013, ...
For k = 4, sequence starts: 19, 131, 431, 811, 991, 2111, 5431, 6011, 10771, ...
etc.
For n > 1, a(n) is congruent to 17 modulo 20.
Number of terms < 10^k: 0, 4, 6, 15, 38, 167, 934, 5091, 30229, ...
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
97 is the lesser in the sexy prime pair (97, 103), and the pair of (97-3)/2 and (103+3)/2 yields another sexy prime pair: (47, 53). Hence 97 is in the sequence.
|
|
|
MATHEMATICA
|
Select[Prime[Range[11000]], AllTrue[Join[{#+6}, (#-3)/2 + {0, 6}], PrimeQ]&] (* Amiram Eldar, Nov 23 2022 *)
|
|
|
PROG
|
(PARI) isok1(p) = isprime(p) && isprime(p+6); \\ A023201
isok(p) = isok1(p) && isok1((p-3)/2); \\ Michel Marcus, Nov 23 2022
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
