A154551 -id:A154551

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A154552

Greater of two consecutive primes, p < q, such that both p*q+p-q and p*q-p+q are prime numbers.

+10
2

3, 5, 29, 509, 997, 1399, 1627, 3307, 4217, 5477, 5689, 6569, 6599, 7369, 7393, 7841, 8191, 8861, 10067, 11311, 11801, 13859, 14401, 15859, 16987, 17851, 18211, 20593, 21101, 24169, 25013, 25339, 25621, 26209, 28019, 28409, 28439, 32009, 35677

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

3*5-2=13; 3*5+2=17, 23*29-6=661; 23*29+6=673...

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

p:= 1: q:= 2: Res:= NULL:

while q < 100000 do

p:= q; q:= nextprime(q);

if isprime(p*q+p-q) and isprime(p*q+q-p) then

Res:= Res, q;

od:

Res; # Robert Israel, May 10 2017

MATHEMATICA

lst={}; Do[pp=Prime[n-1]; p=Prime[n]; d=p-pp; If[PrimeQ[pp*p-d]&&PrimeQ[pp*p+d], AppendTo[lst, p]], {n, 2, 8!}]; lst

pqpQ[{p_, q_}]:=Module[{pq=p*q}, And@@PrimeQ[{pq+p-q, pq-p+q}]]; Transpose[ Select[Partition[Prime[Range[4000]], 2, 1], pqpQ]][[2]] (* Harvey P. Dale, May 20 2012 *)

PROG

(PARI) is(n)=my(p); isprime(n) && isprime((p=precprime(n-1))*n+p-n) && isprime(p*n-p+n) \\ Charles R Greathouse IV, May 10 2017

CROSSREFS

Cf. A138111, A138170, A154550, A154551.

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 11 2009

EXTENSIONS

Edited by Omar E. Pol, Jan 12 2009

STATUS

approved

A154553

Lesser of two consecutive primes, p < q, such that both p*q+p-q and p*q-p+q are prime numbers.

+10
2

2, 3, 23, 503, 991, 1381, 1621, 3301, 4211, 5471, 5683, 6563, 6581, 7351, 7369, 7829, 8179, 8849, 10061, 11299, 11789, 13841, 14389, 15823, 16981, 17839, 18199, 20563, 21089, 24151, 24989, 25321, 25609, 26203, 28001, 28403, 28433, 32003, 35671

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

2*3-1=5;2*3+1=7, 3*5-2=13;3*5+2=17, ...

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..200

MAPLE

with(numtheory); A154553:=proc(q) local a, b, n;

for n from 42676 to q do a:=ithprime(n); b:=nextprime(a);

if isprime(a*b+a-b) and isprime(a*b-a+b) then print(a);

fi; od; end: A154553(10^9); # Paolo P. Lava, May 14 2013