

A103151


Number of decompositions of 2n+1 into 2p+q, where p and q are both odd primes (A065091).


12



0, 0, 0, 1, 1, 2, 1, 3, 2, 2, 2, 3, 3, 4, 2, 4, 2, 4, 4, 4, 4, 5, 3, 4, 6, 5, 3, 6, 3, 3, 6, 6, 5, 7, 3, 4, 7, 6, 5, 8, 3, 7, 7, 7, 4, 10, 5, 6, 9, 5, 5, 11, 5, 6, 9, 7, 6, 10, 7, 5, 11, 8, 6, 10, 5, 6, 12, 8, 5, 12, 5, 9, 12, 8, 6, 13, 7, 6, 11, 9, 9, 16, 4, 8, 12, 9, 9, 13, 7, 6, 13, 11, 8, 16, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,6


COMMENTS

Conjecture: all items for n>=4 are greater than or equal to 1. This is a stronger conjecture than the Goldbach conjecture.


LINKS

R. J. Mathar, Table of n, a(n) for n = 1..10777


EXAMPLE

For 2*4+1 = 9 we have just one such composition: 9 = 2*3+3, so a(4)=1;
For 2*14+1 = 29 we have four such compositions: 29 = 2*3+23 = 2*5+19 = 2*11+7 = 2*13+3, so a(14)=4.


MAPLE

A103151 := proc(n)
local s, a, q;
a := 0 ;
s := 2*n+1 ;
for pi from 2 do
q := s2*ithprime(pi) ;
if q <=2 then
return a ;
else
if isprime(q) then
a := a+1 ;
end if;
end if;
end do:
end proc: # R. J. Mathar, Feb 22 2014


MATHEMATICA

Do[m = 3; ct = 0; While[(m*2) < n, If[PrimeQ[m], cp = n  (2*m); If[ PrimeQ[cp], ct = ct + 1]]; m = m + 2]; Print[ct], {n, 9, 299, 2}]


PROG

(Scheme, with Aubrey Jaffer's SLIB Scheme library from http://www.swiss.ai.mit.edu/~jaffer/SLIB.html )
(define (A103151 n) (let loop ((i 2) (z 0)) (let ((p1 (A000040 i))) (cond ((>= p1 n) z) ((prime? (+ 1 (* 2 ( n p1)))) (loop (+ 1 i) (+ 1 z))) (else (loop (+ 1 i) z))))))


CROSSREFS

A001031, A103152.
Sequence in context: A140720 A033559 A279027 * A035221 A035191 A297167
Adjacent sequences: A103148 A103149 A103150 * A103152 A103153 A103154


KEYWORD

nonn


AUTHOR

Lei Zhou, Feb 09 2005


EXTENSIONS

Edited and Schemecode added by Antti Karttunen, Jun 19 2007


STATUS

approved



