login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A358743
First of three consecutive primes p,q,r such that p+q-r is prime.
4
7, 11, 13, 17, 19, 29, 41, 43, 47, 59, 79, 101, 103, 107, 113, 137, 139, 163, 181, 193, 227, 229, 239, 257, 269, 281, 283, 311, 317, 359, 379, 397, 419, 421, 439, 461, 487, 491, 503, 521, 547, 569, 577, 599, 647, 659, 683, 691, 701, 709, 761, 811, 823, 857, 863, 881, 883, 887, 919, 983, 1019
OFFSET
1,1
COMMENTS
p+q-r is near (and less than) p and odd (for p > 2), so heuristically we would expect it to be prime about 2/log p of the time, yielding around 2x/log^2 x terms up to x. (A more careful analysis of small primes could yield a slightly different leading constant.) - Charles R Greathouse IV, Nov 29 2022
LINKS
EXAMPLE
a(3) = 13 is a prime because 13, 17, 19 are three consecutive primes with 13 + 17 - 19 = 11 prime.
MAPLE
R:= NULL: count:= 0: q:= 2: r:= 3:
while count < 100 do
p:= q; q:= r; r:=nextprime(r);
if isprime(p+q-r) then count:= count+1; R1:= R1, p fi;
od:
R;
MATHEMATICA
Select[Partition[Prime[Range[180]], 3, 1], PrimeQ[#[[1]] + #[[2]] - #[[3]]] &][[;; , 1]] (* Amiram Eldar, Nov 29 2022 *)
PROG
(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen():
p, q, r = 2, 3, 5
while True:
if isprime(p+q-r): yield p
p, q, r = q, r, nextprime(r)
print(list(islice(agen(), 61))) # Michael S. Branicky, Nov 29 2022
(PARI) list(lim)=my(v=List(), p=7, q=11); forprime(r=13, nextprime(nextprime(lim\1+1)+1), if(isprime(p+q-r), listput(v, p)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Nov 29 2022
CROSSREFS
A136720 is a subsequence.
Sequence in context: A293658 A168079 A296928 * A243768 A141636 A214786
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Nov 29 2022
STATUS
approved