A383244 - OEIS

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A383244

Primes of the form p(k)*p(k+1)*(p(k+1) - p(k)) + 1 sorted by increasing k.

4

7, 31, 71, 647, 4003, 6883, 3527, 14947, 34603, 20807, 23327, 173347, 73727, 503869, 103967, 145799, 450403, 194687, 669283, 848203, 1193443, 1775563, 649799, 1976803, 2088547, 2131243, 4687069, 2534947, 2581963, 5338237, 3250123, 3411043, 1555847, 5346763

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OFFSET

1,1

COMMENTS

Conjecture: there are infinitely many such primes.

LINKS

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

MAPLE

q:= 2; R:= NULL: count:= 0:

while count < 100 do

p:= q;

q:= nextprime(q);

v:= p*q*(q-p)+1;

if isprime(v) then R:= R, v; count:= count+1 fi;

od:

R; # Robert Israel, May 11 2025

MATHEMATICA

z = 200; p[n_] := Prime[n];

f[n_] := p[n]*p[n + 1]*(p[n + 1] - p[n])

t1 = Table[f[n] - 1, {n, 1, z}]; (* A383241 *)

t2 = Table[f[n] + 1, {n, 1, z}]; (* A383242 *)

Select[t1, PrimeQ[#] &] (* A383243 *)

Select[t2, PrimeQ[#] &] (* A383244 *)

PROG

(PARI) select(isprime, vector(200, k, prime(k)*prime(k+1)*(prime(k+1) - prime(k)) + 1)) \\ Michel Marcus, May 12 2025

CROSSREFS

Cf. A000042, A383241, A383243.

Primes in A383242.

Sequence in context: A157914 A090684 A383242 * A033199 A304163 A003550

Adjacent sequences: A383241 A383242 A383243 * A383245 A383246 A383247

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 07 2025

STATUS

approved