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%I #20 Sep 08 2022 08:45:30
%S 19,98,218,988,866,2716,1946,5308,12222,5402,20862,18268,10586,24316,
%T 45054,56502,21602,73782,57148,31106,104022,78748,133182,207704,
%U 117628,62426,132316,69986,147868,605486,199708,323262,114266,622330,135002
%N Difference between successive primes cubed: a(n) = prime(n+1)^3 - prime(n)^3.
%H Harvey P. Dale, <a href="/A129701/b129701.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A030078(n+1) - A030078(n). - _Michel Marcus_, Sep 04 2013
%e a(3) because the fourth prime is 7, cubed 343, the third prime is 5, cubed 125, 343-125=218.
%p last:=8;for i from 3 to 30 do > while isprime(i)=false do > i:=i + 1; > end do; > r:= i^3 - last; > last:=i^3; > end do;
%t Table[Prime[n+1]^3 - Prime[n]^3, {n, 1, 40}] (* _Stefan Steinerberger_, Jun 05 2007 *)
%t Last[#]-First[#]&/@(Partition[Prime[Range[40]],2,1]^3) (* _Harvey P. Dale_, Oct 13 2012 *)
%o (PARI) {a(n) = prime(n+1)^3 - prime(n)^3}; \\ _G. C. Greubel_, May 19 2019
%o (Magma) [NthPrime(n+1)^3 - NthPrime(n)^3: n in [1..40]]; // _G. C. Greubel_, May 19 2019
%o (Sage) [nth_prime(n+1)^3 - nth_prime(n)^3 for n in (1..40)] # _G. C. Greubel_, May 19 2019
%Y Cf. A030078 (cubes of primes).
%K nonn
%O 1,1
%A _Ben Paul Thurston_, Jun 01 2007
%E More terms from _Stefan Steinerberger_, Jun 05 2007
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