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 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 := s-2*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 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 Scheme-code added by Antti Karttunen, Jun 19 2007 STATUS approved

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Last modified May 15 04:03 EDT 2021. Contains 343909 sequences. (Running on oeis4.)