|
%I #8 Jun 18 2021 16:07:36
%S -1,2,8,14,20,27,37,46,57,70,80,95,108,124,142,160,174,193,213,231,
%T 253,277,297,321,346,376,396,425,451,476,507,537,566,598,626,659,693,
%U 725,770,796,836,870,912,941,984,1022,1060,1103,1146,1187,1243,1277,1322,1366,1404,1449,1500,1553,1597,1648,1691,1746,1798
%N Smallest index-sum i+j such that prime(i) + prime(j) = 4*n^2. a(0)=-1 to indicate that there is no such pair of primes.
%F a(n)= min(i+j), 1<=i<=j: A000040(i)+A000040(j)=A016742(n). - _R. J. Mathar_, Apr 22 2008
%p A133229 := proc(n) local a016742,i,j,a ; a016742 := 4*n^2 ; a := 2*numtheory[pi](a016742) ; if n =0 then RETURN(-1) ; fi ; for i from 1 to numtheory[pi](a016742-1) do if isprime(a016742-ithprime(i)) then j := numtheory[pi](a016742-ithprime(i)) : a := min(a,i+j) ; fi ; od: RETURN(a) ; end: seq(A133229(n),n=0..80) ; # _R. J. Mathar_, Apr 22 2008
%t Join[{-1},Table[Min[Total/@(PrimePi/@Select[IntegerPartitions[4 n^2, {2}],AllTrue[ #,PrimeQ]&])],{n,70}]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 18 2021 *)
%Y Cf. A000040, A005843, A016742, A113631, A133230.
%K sign
%O 0,2
%A _Alexander R. Povolotsky_, Dec 19 2007
%E Edited and extended by _R. J. Mathar_, Apr 22 2008
|
