A306190 a(n) = p^2 - p - 1 where p = prime(n), the n-th prime.

1, 5, 19, 41, 109, 155, 271, 341, 505, 811, 929, 1331, 1639, 1805, 2161, 2755, 3421, 3659, 4421, 4969, 5255, 6161, 6805, 7831, 9311, 10099, 10505, 11341, 11771, 12655, 16001, 17029, 18631, 19181, 22051, 22649, 24491, 26405, 27721, 29755, 31861, 32579, 36289

Offset

1,2

Comments

Terms are divisible by 5 iff p is of the form 10*m + 3 (A030431).

Links

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

Formula

a(n) = A036689(n) - 1.

a(n) = A036690(n) - A072055(n).

a(n) = A060800(n) - A089241(n).

From Amiram Eldar, Nov 07 2022: (Start)

Product_{n>=1} (1 + 1/a(n)) = A065488.

Product_{n>=2} (1 - 1/a(n)) = A065479. (End)

a(n) = A033879(A001248(n)). [Deficiency of squares of primes] - Antti Karttunen, Dec 13 2024

Example

a(3) = 19 because 5^2 - 5 - 1 = 19.

Maple

map(p -> p^2-p-1, [seq(ithprime(i), i=1..100)]); # Robert Israel, Mar 11 2019

Mathematica

Table[Prime[n]^2-Prime[n]-1, {n, 1, 100}] (* Jinyuan Wang, Feb 02 2019 *)

Prog

(PARI) a(n) = {p=prime(n); p^2-p-1; } \\ Jinyuan Wang, Feb 02 2019

Crossrefs

Supersequence of A091568.

Subsequence of A028387 or A165900.

Second column of A378979.

Cf. A000040, A001248, A030431, A033879, A036689, A036690, A060800, A065479, A065488, A072055, A089241.

A039914 is an essentially identical sequence.

Sequence in context: A155737 A100572 A119534 * A033622 A091568 A147307

Adjacent sequences: A306187 A306188 A306189 * A306191 A306192 A306193

Keyword

nonn

Author

Kritsada Moomuang, Jan 28 2019

Status

approved