A341937 - OEIS

%I #9 Oct 29 2023 17:19:17

%S 17,37,59,89,167,233,439,439,683,1021,5807,10427,13043,12569,19163,

%T 36887,40493,64579,66587,86291,103699,124693,126839,179743,218137,

%U 329627,419927,437113,472133,606997,621031,660917,695771,731033,741569,772649,783701,793673,848273,868639,898823,999959

%N Primes 2*p*q-2*q*r+r*s where p,q,r,s are consecutive primes.

%C a(k) = 2*p*q-2*q*r+r*s where p = A341934(k) and p,q,r,s are consecutive primes.

%H Robert Israel, <a href="/A341937/b341937.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 167 because A341934(5) = 11 and (p,q,r,s)=(11,13,17,19) are consecutive primes with 2*p*q-2*q*r+r*s = 167.

%p P:= select(isprime, [2, seq(i, i=3..10000, 2)]):

%p B:= select(i -> isprime(P[i+2]*P[i+3]-2*P[i+1]*(P[i+2]-P[i])), [$1..nops(P)-3]):

%p seq(P[i+2]*P[i+3]-2*P[i+1]*(P[i+2]-P[i]), i = B);

%t Select[2#[[1]]#[[2]]-2#[[2]]#[[3]]+#[[3]]#[[4]]&/@Partition[Prime[Range[200]],4,1],PrimeQ] (* _Harvey P. Dale_, Oct 29 2023 *)

%Y Cf. A341934.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 23 2021