A328464 -id:A328464 - cp's OEIS frontend

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

Antti Karttunen, Jun 28 2017

nonn

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

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

Row 6 of A286625 (column 6 of A286623). Column 4 of A328464.
One more than A123134.
Cf. A000040, A023523, A180932 (primes in this sequence).

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

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

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

a(n) = (A000040(1+n)*A000040(n)) + A000040(n) + 1.
a(n) = 1 + A123134(n).
a(n) = A000040(n) + A023523(1+n).

A328462 Numbers obtained by reinterpreting base-2 representation of odd numbers in primorial base.

Original entry on oeis.org

1, 3, 7, 9, 31, 33, 37, 39, 211, 213, 217, 219, 241, 243, 247, 249, 2311, 2313, 2317, 2319, 2341, 2343, 2347, 2349, 2521, 2523, 2527, 2529, 2551, 2553, 2557, 2559, 30031, 30033, 30037, 30039, 30061, 30063, 30067, 30069, 30241, 30243, 30247, 30249, 30271, 30273, 30277, 30279, 32341, 32343, 32347, 32349, 32371, 32373

Offset: 1

Antti Karttunen, Oct 16 2019

Cf. A002110, A007814.
Row 1 of A328464, odd bisection of A276156 and of A328461.
Cf. A143293 (subsequence).

A276156(n) = { my(p=2,pr=1,s=0); while(n,if(n%2,s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };
A328462(n) = A276156(n+n-1);

cp's OEIS Frontend

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

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