A063036 Difference between average of smallest prime greater than n^3 and largest prime less than (n+1)^3 and n-th pronic [=n(n+1)].

11, 33, 70, 139, 238, 372, 552, 775, 1058, 1410, 1800, 2290, 2851, 3501, 4232, 5067, 6006, 7048, 8213, 9496, 10901, 12450, 14124, 15951, 17928, 20059, 22358, 24822, 27470, 30284, 33296, 36504, 39898, 43514, 47325, 51364, 55597, 60105, 64822

Offset

2,1

Comments

First term is not an integer.

Links

Harry J. Smith, Table of n, a(n) for n = 2..1000

Example

n=4: a(4) = 70 because the smallest prime greater than 4^3 is 67, the largest prime less than 5^3 is 113, the average of 67 and 113 is 90, and 90 - 4*5 = 70.

Mathematica

Table[Mean[{NextPrime[n^3], NextPrime[(n+1)^3, -1]}]-n(n+1), {n, 2, 40}] (* Harvey P. Dale, Feb 21 2022 *)

Prog

(PARI) j=[]; for(n=2, 60, j=concat(j, ((precprime((n+1)^3)+nextprime(n^3))/2)- (n*(n+1))))); j
(PARI) { for (n=2, 1000, a=(precprime((n + 1)^3) + nextprime(n^3))/2 - n*(n + 1); write("b063036.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 16 2009

Crossrefs

Sequence in context: A296543 A152740 A080859 * A163673 A212132 A027025

Adjacent sequences: A063033 A063034 A063035 * A063037 A063038 A063039

Keyword

easy,nonn

Author

Jason Earls, Aug 03 2001

Status

approved