The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A339640 a(n) = (A062772(n) + A054270(n)) / 2 - A001248(n). 0
 0, 0, 1, 1, -1, 1, -1, 2, 3, 5, -1, 1, 0, 5, 1, 2, -1, 2, -1, 4, -1, -3, 2, 2, -1, 1, 1, 8, -4, 3, 4, 2, -4, 5, 10, -4, -4, -2, -1, 8, -1, -1, 5, -1, 3, -7, 4, 4, 1, 2, 1, 4, 5, 8, 8, 8, -1, 2, -4, -2, 3, 1, -8, -4, 1, -1, -4, 10, -2, 15, 8, 10, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Conjecture: The partial sums of this sequence are greater than or equal to zero. This means that the squares of the prime numbers are smaller than the average of the previous and the next prime number most of the time. LINKS FORMULA a(n) = (nextprime(prime(n)^2) + precprime(prime(n)^2)) / 2 - prime(n)^2. EXAMPLE For n = 10 prime(10)^2 = 29^2 = 841. The previous prime of 841 is 839 and the next 853. The average of 839 and 853 is (839 + 853)/2 = 846. So a(10) = 846 - 841 = 5. MATHEMATICA Array[(Total@ NextPrime[#, {-1, 1}])/2 - # &[Prime[#]^2] &, 73] (* Michael De Vlieger, Dec 11 2020 *) PROG (PARI) forprime(n = 2, 370, print1((nextprime(n^2) + precprime(n^2)) / 2 - n^2", ")) CROSSREFS Cf. A000040, A001248, A054270, A062772, A123993. Sequence in context: A031067 A300392 A335706 * A031027 A134730 A126046 Adjacent sequences:  A339637 A339638 A339639 * A339641 A339642 A339643 KEYWORD sign AUTHOR Dimitris Valianatos, Dec 11 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 17 23:00 EST 2021. Contains 340247 sequences. (Running on oeis4.)