login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A347008 Numbers that can be written in exactly two ways as p*q+p+q where p and q are primes with p < q. 1
23, 47, 119, 167, 179, 323, 407, 419, 527, 587, 639, 647, 879, 935, 1043, 1103, 1119, 1139, 1215, 1223, 1247, 1271, 1331, 1367, 1403, 1455, 1595, 1599, 1631, 1691, 1775, 1791, 1859, 1895, 1931, 1943, 1959, 1967, 1979, 2099, 2111, 2175, 2183, 2219, 2231, 2435, 2471, 2483, 2495, 2543, 2559, 2603 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..5000

EXAMPLE

a(3) = 119 is a term because 119 = 5*19+5+19 = 3*29+3+29 are the two ways to produce 119 = p*q+p+q with primes p < q.

MAPLE

N:= 10000: # to produce terms <= N

R:= Vector(N):

P:= select(isprime, [2, seq(i, i=3..N/3, 2)]):

for i from 1 to nops(P) do

for j from 1 to i-1 do

v:=P[i]*P[j]+P[i]+P[j];

if v <= N then R[v]:= R[v]+1 fi

od od:

select(t -> R[t]=2, [$1..N]);

PROG

(Python)

from sympy import primerange

from collections import Counter

def aupto(limit):

primes = list(primerange(2, limit//3+1))

nums = [p*q+p+q for i, p in enumerate(primes) for q in primes[i+1:]]

counts = Counter([k for k in nums if k <= limit])

return sorted(k for k in counts if counts[k] == 2)

print(aupto(2604)) # Michael S. Branicky, Aug 10 2021

CROSSREFS

Cf. A198277.

Sequence in context: A043197 A043977 A042048 * A239563 A241207 A042050

Adjacent sequences: A347005 A347006 A347007 * A347009 A347010 A347011

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Aug 10 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 09:49 EST 2022. Contains 358423 sequences. (Running on oeis4.)