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A154553 Lesser of two consecutive primes, p < q, such that both p*q+p-q and p*q-p+q are prime numbers. 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

MATHEMATICA

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

pnQ[{p_, q_}]:=And@@PrimeQ[{p*q+p-q, p*q-p+q}]; Transpose[Select[ Partition[ Prime[Range[4000]], 2, 1], pnQ]][[1]] (* Harvey P. Dale, Jul 12 2012 *)

CROSSREFS

Cf. A138111, A138170, A154550, A154551, A154552

Sequence in context: A104458 A191859 A289550 * A160341 A092388 A225726

Adjacent sequences:  A154550 A154551 A154552 * A154554 A154555 A154556

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 11 2009

EXTENSIONS

Edited by Omar E. Pol, Jan 12 2009

STATUS

approved

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Last modified February 29 01:30 EST 2020. Contains 332353 sequences. (Running on oeis4.)