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A024702 a(n) = (prime(n)^2 - 1)/24. 25
1, 2, 5, 7, 12, 15, 22, 35, 40, 57, 70, 77, 92, 117, 145, 155, 187, 210, 222, 260, 287, 330, 392, 425, 442, 477, 495, 532, 672, 715, 782, 805, 925, 950, 1027, 1107, 1162, 1247, 1335, 1365, 1520, 1552, 1617, 1650, 1855, 2072, 2147, 2185, 2262, 2380, 2420, 2625, 2752, 2882, 3015 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

COMMENTS

For n>3 and m>1, a(n) = A000330(m)/(2m+1), for m such that 2m+1 = prime, which results in 2m+1 = prime(n). For example, for m = 8, 2m+1 = 17 = prime(7), A000330(8) = 204, 204/17 = 12 = a(7). - Richard R. Forberg, Aug 20 2013

For primes => 5, a(n) mod 5 = {0,2}. - Richard R. Forberg, Aug 28 2013

The only primes in this sequence are 2, 5 and 7 (checked up to n = 10^7). The set of prime factors, however, appears to include all primes. - Richard R. Forberg, Feb 28 2015

Subsequence of generalized pentagonal numbers (cf. A001318): a(n) = k_n*(3*k_n-1)/2, for k_n in {1, -1, 2, -2, 3, -3, 4, 5, -5, -6, 7, -7, 8, 9, 10, -10, ... } = A024699(n-2) * ([A000040(n) mod 6] - 3) / 2, n >= 3. - Daniel Forgues, Aug 02 2016

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 3..10000

FORMULA

a(n) = (A000040(n)^2 - 1)/24 = (A001248(n) - 1)/24. - Omar E. Pol, Dec 07 2011

a(n) = A005097(n-1)*A006254(n-1)/6. - Bruno Berselli, Dec 08 2011

a(n) = A084920(n)/24. - R. J. Mathar, Aug 23 2013

EXAMPLE

For n=6, the 6th prime is 13, so a(6) = (13^2 - 1)/24 = 168/24 = 7. Note that p^2 - 1 is always divisible by 24 since p == 1 or 2 (mod 3), so p^2 == 1 (mod 3) and p == 1, 3, 5, or 7 (mod 8) so p^2 == 1 (mod 8). - Michael B. Porter, Sep 02 2016

MAPLE

A024702:=n->(ithprime(n)^2-1)/24: seq(A024702(n), n=3..70); # Wesley Ivan Hurt, Mar 01 2015

MATHEMATICA

(Prime[Range[3, 100]]^2-1)/24 (* Vladimir Joseph Stephan Orlovsky, Mar 15 2011 *)

PROG

(PARI) a(n)=prime(n)^2\24 \\ Charles R Greathouse IV, May 30 2013

(PARI) is(n)=my(k); issquare(24*n+1, &k)&&isprime(k) \\ Charles R Greathouse IV, May 31 2013

CROSSREFS

Subsequence of generalized pentagonal numbers A001318.

Cf. A075888.

Sequence in context: A088822 A080182 A001318 * A226084 A161664 A080547

Adjacent sequences:  A024699 A024700 A024701 * A024703 A024704 A024705

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 11 1999

STATUS

approved

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Last modified May 28 21:38 EDT 2017. Contains 287241 sequences.