A286624 a(n) = (prime(1+n)*prime(n)) + prime(n) + 1.

9, 19, 41, 85, 155, 235, 341, 457, 691, 929, 1179, 1555, 1805, 2065, 2539, 3181, 3659, 4149, 4825, 5255, 5841, 6637, 7471, 8723, 9895, 10505, 11125, 11771, 12427, 14465, 16765, 18079, 19181, 20851, 22649, 23859, 25749, 27385, 29059, 31141, 32579, 34753, 37055, 38215, 39401, 42189, 47265, 50845, 52211

Offset: 1

Author

Antti Karttunen, Jun 28 2017

Keywords

• nonn

Comments

9 is the only perfect square in this sequence. - Altug Alkan, Jul 01 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Row 6 of A286625 (column 6 of A286623). Column 4 of A328464.

One more than A123134.

Cf. A000040, A023523, A180932 (primes in this sequence).

Programs

Mathematica

Array[(#1 #2) + #1 + 1 & @@ Prime[# + {0, 1}] &, 49] (* Michael De Vlieger, Mar 14 2021 *)

PARI

lista(nn) = forprime(p=2, nn, print1(p*(nextprime(p+1)+1)+1, ", ")); \\ Altug Alkan, Jul 01 2017

Scheme

(define (A286624 n) (+ (* (A000040 (+ 1 n)) (A000040 n)) (A000040 n) 1))
(define (A286624 n) (+ 1 (* (+ 1 (A000040 (+ 1 n))) (A000040 n))))

Formula

a(n) = (A000040(1+n)*A000040(n)) + A000040(n) + 1.

a(n) = 1 + A123134(n).

a(n) = A000040(n) + A023523(1+n).