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 A062021 a(n) = Sum_{i=1..n} Sum_{j=1..i} (prime(i)^2 - prime(j)^2). 3
 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) - a(n-2) + (n-1)*(prime(n)^2 - prime(n-1)^2) with a(1) = 0, a(2) = 5. EXAMPLE a(3) = (5^2 - 2^2) + (5^2 - 3^2) + (3^2 - 2^2) = 42. 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]-a[n-2]+(n-1)(Prime[n]^2 - Prime[n-1]^2)}, a, {n, 40}] (* Harvey P. Dale, May 16 2019 *) PROG (Magma) [(&+[(&+[NthPrime(i)^2 - NthPrime(j)^2: j in [1..i]]): i in [1..n]]): n in [1..40]]; // G. C. Greubel, May 04 2022 (SageMath) @CachedFunction def a(n): if (n<3): return 5*(n-1) else: return 2*a(n-1) - a(n-2) + (n-1)*(nth_prime(n)^2 - nth_prime(n-1)^2) [a(n) for n in (1..40)] # G. C. Greubel, May 04 2022 CROSSREFS Cf. A000040, A062020, A062022. 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 Name edited by G. C. Greubel, May 04 2022 STATUS approved

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Last modified November 29 16:39 EST 2022. Contains 358431 sequences. (Running on oeis4.)