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

Author

Kritsada Moomuang, Jan 28 2019

Keywords

• nonn

Comments

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

Examples

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

Links

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

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.

Programs

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 *)

PARI

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

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