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A298704 Numbers that are the smallest of four consecutive primes, no two of which, along with the product of the other two, sum to a nonprime. 1
10942177, 33612487, 38370391, 350212139, 431472421, 594652609, 616335793, 795968851, 867683191, 885354367, 982828577, 1058353099, 1278213241, 1367427883, 1966024733, 2329521127, 2734073753, 2959246399, 3067739581 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Hans Havermann, Table of n, a(n) for n = 1..800

EXAMPLE

10942177, 10942187, 10942201, 10942207 are four consecutive primes. The six ways of adding the product of two of these to the sum of the other two yields 119731368805507, 119731521995971, 119731587649027, 119731631417971, 119731697071087, 119731850261971, all of which are prime. So 10942177 is a term of the sequence.

MAPLE

with(numtheory): with(combinat):

P:=proc(q) local a, b, c, d, k, n, ok, x, y;

a:=0; b:=10942177; c:=10942187; d:=10942201;

for n from 1 to q do ok:=1; a:=b; b:=c; c:=d;

d:=nextprime(d); x:={a, b, c, d}; y:=choose(x, 2);

for k from 1 to 6 do if not isprime(convert(y[k], `*`)+convert(x minus y[k], `+`)) then ok:=0; break; fi; od; if ok=1 then print(a); fi; od; end: P(10^20); # Paolo P. Lava, Jan 25 2018

CROSSREFS

Sequence in context: A205464 A202470 A224639 * A308079 A114680 A329224

Adjacent sequences:  A298701 A298702 A298703 * A298705 A298706 A298707

KEYWORD

nonn

AUTHOR

Hans Havermann, Jan 24 2018

STATUS

approved

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Last modified May 14 18:47 EDT 2021. Contains 343900 sequences. (Running on oeis4.)