A048852 Difference between b^2 (in c^2=a^2+b^2) and product of successive prime pairs.

0, 3, 10, 14, 44, 26, 68, 38, 92, 174, 62, 222, 164, 86, 188, 318, 354, 122, 402, 284, 146, 474, 332, 534, 776, 404, 206, 428, 218, 452, 1778, 524, 822, 278, 1490, 302, 942, 978, 668, 1038, 1074, 362, 1910, 386, 788, 398, 2532, 2676, 908, 458, 932, 1434, 482

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Formula

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.

For n>0, a(n) = A000040(n+1)^2 - A000040(n) * A000040(n+1). - Mamuka Jibladze, Mar 24 2017

Example

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.

Mathematica

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 *)

Prog

(Magma) [0] cat [NthPrime(n+1)*(NthPrime(n+1)-NthPrime(n)): n in [1..60]]; // G. C. Greubel, Feb 22 2024
(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

Crossrefs

Cf. A000040, A048851, A006094, A291463.

Sequence in context: A024593 A128930 A328091 * A226101 A141463 A134102

Adjacent sequences: A048849 A048850 A048851 * A048853 A048854 A048855

Keyword

easy,nonn

Author

Enoch Haga

Status

approved