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A062021 Let P(n) = { 2,3,5,7,...,p(n) } where p(n) is n-th prime; then a(1) =0 and a(n) = Sum [mod{p(i)^2 - p(j)^2}], for all i and j from 1 to n. 1
0, 5, 42, 151, 548, 1185, 2542, 4403, 7608, 13621, 20834, 32535, 47980, 65609, 88278, 119947, 162368, 208869, 269194, 340007, 416580, 512305, 622286, 756003, 925432, 1114661, 1314498, 1537015, 1771628, 2031993, 2393158, 2786315 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

a(n) = 2*a(n-1) + (n-1)*(p(n)^2-p(n-1)^2) - a(n-2)

EXAMPLE

a(3) = (5^2-2^2) + (5^2-3^2) + (3^2-2^2) = 42, P(3) = {2,3,5}.

MAPLE

N:= 100: # for a(1)..a(N)

P2:= [seq(ithprime(i)^2, i=1..N)]:

DP2:= P2[2..-1]-P2[1..-2]:

A[1]:= 0: A[2]:= 5:

for n from 3 to N do A[n]:= 2*A[n-1]+(n-1)*DP2[n-1]-A[n-2] od:

seq(A[i], i=1..N); # Robert Israel, Feb 02 2020

MATHEMATICA

RecurrenceTable[{a[1]==0, a[2]==5, a[n]==2a[n-1]+(n-1)(Prime[n]^2-Prime[ n-1]^2)-a[n-2]}, a, {n, 40}] (* Harvey P. Dale, May 16 2019 *)

CROSSREFS

Sequence in context: A222474 A327269 A266021 * A241780 A215785 A082145

Adjacent sequences:  A062018 A062019 A062020 * A062022 A062023 A062024

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jun 02 2001

EXTENSIONS

More terms and formula from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

STATUS

approved

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Last modified August 3 11:54 EDT 2020. Contains 336198 sequences. (Running on oeis4.)