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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 * A309952 A059252 A251619 Adjacent sequences:  A269040 A269041 A269042 * A269044 A269045 A269046 KEYWORD nonn AUTHOR Michel Lagneau, Feb 18 2016 STATUS approved

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Last modified May 12 09:16 EDT 2021. Contains 343821 sequences. (Running on oeis4.)