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%I #12 Aug 18 2024 20:16:17
%S 1,4,4,28,12,11,10,30,27,26,27,27,78,25,24,20,21,25,177,73,68,72,72,
%T 178,71,72,69,70,181,176,69,68,66,66,65,175,429,61,40,448,44,45,51,47,
%U 420,426,173,427,425,1062,1072,429,428,1071,1067,430,165,164,426,162
%N Least number k such that k divides the average of prime(k-n) and prime(k+n).
%C Up to n = 75, I have found no multiple > 12.
%H Harry J. Smith, <a href="/A066836/b066836.txt">Table of n, a(n) for n = 0..1000</a>
%e For a(3) we wish to find a k such that the average of Pi(k+3) + Pi(k-3) is a multiple of k. The least k that meets this criterion is 28. (Pi(31) + Pi(25))/2 is (127 + 97)/2 = 112 = 4*28.
%t b = {}; Do[ a = Table[ Prime[ i ], {i, 1, 2n + 1} ]; k = 2n + 1; While[ !IntegerQ[ (a[ [ 1 ] ] + a[ [ -1 ] ])/(2(k - n)) ], k++; a = Append[ a, Prime[ k ] ]; a = Drop[ a, 1 ] ]; b = Append[ b, k - n ], {n, 0, 75} ]; b
%o (PARI) { default(primelimit, 4294965247); for (n=0, 1000, b=0; k=n; while(b==0, k++; if ((prime(k-n) + prime(k+n)) % (2*k) == 0, b=1)); write("b066836.txt", n, " ", k) ) } \\ _Harry J. Smith_, Mar 31 2010
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Jan 20 2002
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