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%I #20 Feb 22 2024 20:22:04
%S 0,3,10,14,44,26,68,38,92,174,62,222,164,86,188,318,354,122,402,284,
%T 146,474,332,534,776,404,206,428,218,452,1778,524,822,278,1490,302,
%U 942,978,668,1038,1074,362,1910,386,788,398,2532,2676,908,458,932,1434,482
%N Difference between b^2 (in c^2=a^2+b^2) and product of successive prime pairs.
%H G. C. Greubel, <a href="/A048852/b048852.txt">Table of n, a(n) for n = 0..10000</a>
%F Find b^2 in Pythagorean formula c^2=a^2+b^2. Subtract product of successive prime pair at same a(n) beginning at 2*2.
%F For n>0, a(n) = A000040(n+1)^2 - A000040(n) * A000040(n+1). - _Mamuka Jibladze_, Mar 24 2017
%e a(3)=10. Product of 3rd prime pair 3*5=15 (after 2*2=4 and 2*3=6). b^2=25 (in c^2=a^2+b^2) where c^2=34 and a^2=9. Then 25-15=10.
%t With[{P=Prime}, Table[If[n==0, 0, P[n+1]*(P[n+1]-P[n])], {n,0,60}]] (* _G. C. Greubel_, Feb 22 2024 *)
%o (Magma) [0] cat [NthPrime(n+1)*(NthPrime(n+1)-NthPrime(n)): n in [1..60]]; // _G. C. Greubel_, Feb 22 2024
%o (SageMath) p=nth_prime; [0]+[p(n+1)*(p(n+1)-p(n)) for n in range(1,61)] # _G. C. Greubel_, Feb 22 2024
%Y Cf. A000040, A048851, A006094, A291463.
%K easy,nonn
%O 0,2
%A _Enoch Haga_
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