cp's OEIS Frontend

A062357 a(n) = n*p(n+1)-(n+1)*p(n) = n*d(n)-p(n), where p(n) is the n-th prime and d(n) is the n-th prime-difference, A001223(n).

%I A062357 #19 Sep 08 2022 08:45:03
%S A062357 -1,1,1,9,-1,11,-3,13,31,-9,35,11,-15,13,43,43,-25,47,9,-31,53,9,55,
%T A062357 103,3,-49,5,-51,7,307,-3,61,-71,201,-79,65,65,-11,67,67,-97,239,-105,
%U A062357 -17,-107,353,353,-31,-129,-29,73,-135,289,73,73,73,-155,77,-41,-161,327,575,-55,-183,-53,607,71,343,-209,-69,73,217
%N A062357 a(n) = n*p(n+1)-(n+1)*p(n) = n*d(n)-p(n), where p(n) is the n-th prime and d(n) is the n-th prime-difference, A001223(n).
%C A062357 A sequence based on the solution of the equation: 1+(1+n)*prime(n)/x-n*prime(n+1)/x=0 for x. This is an irrational rotation-like sequence: the sequence is similar to a Beatty sequence. - _Roger L. Bagula_, Jun 06 2002
%H A062357 Harry J. Smith, <a href="/A062357/b062357.txt">Table of n, a(n) for n = 1..1000</a>
%F A062357 a(n) = n*A000040(n+1) - (n+1)*A000040(n) = n*A001223(n) - A000040(n).
%e A062357 n = 10: a(10) = 10*31-11*29 = 310-319 = -9;
%e A062357 n = 54: a(54) = 54*257-55*251 = 13878-13805 = 73;
%e A062357 n = 55: a(55) = 55*263-56*257 = 14465-14392 = 73; consecutive terms are often equal to each other.
%p A062357 seq(n*ithprime(n+1)-(n+1)*ithprime(n),n=1..80); # _Muniru A Asiru_, Jun 29 2018
%t A062357 Table[(Prime[w+1]-Prime[w])*w-Prime[w], {w, 1, 1024}]
%o A062357 (PARI) a(n)={n*prime(n + 1) - (n + 1)*prime(n)} \\ _Harry J. Smith_, Aug 06 2009
%o A062357 (Magma) [n*NthPrime(n + 1) - (n + 1)*NthPrime(n): n in [1..75]]; // _Vincenzo Librandi_, Jun 29 2018
%Y A062357 Cf. A000040, A001223, A062742, A062743.
%K A062357 sign,easy
%O A062357 1,4
%A A062357 _Labos Elemer_, Jul 13 2001