A133229 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.

-1, 2, 8, 14, 20, 27, 37, 46, 57, 70, 80, 95, 108, 124, 142, 160, 174, 193, 213, 231, 253, 277, 297, 321, 346, 376, 396, 425, 451, 476, 507, 537, 566, 598, 626, 659, 693, 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

Offset

0,2

Links

Table of n, a(n) for n=0..62.

Formula

a(n)= min(i+j), 1<=i<=j: A000040(i)+A000040(j)=A016742(n). - R. J. Mathar, Apr 22 2008

Maple

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

Mathematica

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 *)

Crossrefs

Cf. A000040, A005843, A016742, A113631, A133230.

Sequence in context: A294960 A101959 A241003 * A364615 A161330 A046940

Adjacent sequences: A133226 A133227 A133228 * A133230 A133231 A133232

Keyword

sign

Author

Alexander R. Povolotsky, Dec 19 2007

Extensions

Edited and extended by R. J. Mathar, Apr 22 2008

Status

approved