A240860 -id:A240860 - cp's OEIS frontend

A339957 Primes in A240860 (up to sign).

5, 29, 149, 461, 1637, 1877, 4373, 13037, 13757, 32309, 41381, 43853, 63533, 69821, 92333, 154157, 174917, 228869, 250949, 358637, 381917, 388757, 565661, 587693, 651293, 697973, 755861, 790613, 862061, 985613, 1127309, 1180637, 1303613, 1739981, 2147693, 2345261, 2586989, 2684837, 2876261

Offset: 1

J. M. Bergot and Robert Israel, Dec 24 2020

nonn

			a(3) = 149 is in the sequence because it is prime and A240860(8) = -149.

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

Cf. A240860.

R:= NULL: count:= 0:
v:= 0: p:= 1:
while count < 100 do
  p:= nextprime(p);
  v:= p^2 - v;
  if isprime(v) then R:= R, v; count:= count+1 fi
od:
R;

A242188 a(n) = Sum_{i=1..n} (-1)^(i+1) prime(i)^3.

Original entry on oeis.org

0, 8, -19, 106, -237, 1094, -1103, 3810, -3049, 9118, -15271, 14520, -36133, 32788, -46719, 57104, -91773, 113606, -113375, 187388, -170523, 218494, -274545, 297242, -407727, 504946

Offset: 0

Timothy Varghese, May 22 2014

sign

For n even this is the negative of the sum of (3^3 - 2^3) + (7^3 - 5^3) + .. (prime(n)^3 - prime(n-1)^3). But this is half of the terms in the sum of (3^3 - 2^3) + (5^3 - 3^3) + (7^3 - 5^3) + ... + (prime(n)^3 - prime(n-1)^3) which has a sum that telescopes to prime(n)^3 - 8. Thus a good estimate of a(n) (half the terms) is prime(n)^3/2 (half the square of the n-th prime) which works well. For odd n, add prime(n)^2 to the estimate for even n.

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A008347, A240860.

ListTools:-PartialSums([0,seq((-1)^(i+1)*ithprime(i)^3, i=1..40)]); # Robert Israel, Mar 09 2020

Table[Sum[(-1)^(i+1) Prime[i]^3,{i,n}],{n,0,30}] (* Harvey P. Dale, May 16 2021 *)

a(n) = sum(i=1, n, (-1)^(i+1)*prime(i)^3);

cp's OEIS Frontend

A339957 Primes in A240860 (up to sign).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple