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A269043 a(n) is the number of distinct values that can be expressed as prime(n+k) + prime(n-k) in at least 2 different ways. 2
0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 2, 2, 3, 1, 4, 4, 2, 4, 4, 4, 3, 5, 5, 7, 9, 8, 7, 8, 7, 6, 7, 9, 7, 9, 8, 11, 8, 8, 7, 10, 9, 11, 12, 9, 9, 14, 11, 12, 11, 15, 15, 12, 14, 12, 12, 17, 11, 14, 15, 15, 14, 15, 18, 16, 13, 18, 12, 16, 14, 16, 14, 12, 19, 17, 13, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Conjecture: a(n) > 0 for n > 3.

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..1000

EXAMPLE

a(13) = 3 because:

p(13 + 1)  + p(13 - 1)  = 43 + 37 = 80;

p(13 + 2)  + p(13 - 2)  = 47 + 31 = 78;

p(13 + 3)  + p(13 - 3)  = 53 + 29 = 82;

p(13 + 4)  + p(13 - 4)  = 59 + 23 = 82;

p(13 + 5)  + p(13 - 5)  = 61 + 19 = 80;

p(13 + 6)  + p(13 - 6)  = 67 + 17 = 84;

p(13 + 7)  + p(13 - 7)  = 71 + 13 = 84;

p(13 + 8)  + p(13 - 8)  = 73 + 11 = 84.

p(13 + 9)  + p(13 - 9)  = 79 + 7  = 86;

p(13 + 10) + p(13 - 10) = 83 + 5  = 88;

p(13 + 11) + p(13 - 11) = 89 + 3  = 92;

p(13 + 12) + p(13 - 12) = 97 + 2  = 99.

The 3 distinct values of prime(n+k) + prime(n-k) that are each obtained in at least 2 ways are 80, 82 and 84.

MAPLE

for n from 1 to 100 do:

  lst:={}:W:=array(1..n-1):cr:=0:

    for m from n-1 by -1 to 1 do:

      q:=ithprime(n-m)+ithprime(n+m):lst:=lst union {q}:W[m]:=q:

    od:

      n0:=nops(lst):c:=0:U:=array(1..n0):

        for i from 1 to n0 do:

         c1:=0:

         for j from 1 to n-1 do:

          if lst[i]=W[j] then c:=c+1:c1:=c1+1:

          else fi:

         od:

        U[i]:=c1:cr:=cr+1:

       od:

       ct:=0:

       for l from 1 to cr do:

       if U[l]>1 then ct:=ct+1:

       else fi:

       od:

       printf(`%d, `, ct):

od:

PROG

(PARI) a(n) = {v = []; for (k=1, n-1, v = concat(v, prime(n+k) + prime(n-k)); ); vd = vecsort(v, , 8); sum(k=1, #vd, #select(x->x==vd[k], v)>1); } \\ Michel Marcus, Mar 13 2016

CROSSREFS

Cf. A006562, A055380, A055382.

Sequence in context: A048466 A096838 A096007 * A059252 A251619 A030620

Adjacent sequences:  A269040 A269041 A269042 * A269044 A269045 A269046

KEYWORD

nonn

AUTHOR

Michel Lagneau, Feb 18 2016

STATUS

approved

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Last modified August 23 22:20 EDT 2019. Contains 326254 sequences. (Running on oeis4.)