A066836 Least number k such that k divides the average of prime(k-n) and prime(k+n).

1, 4, 4, 28, 12, 11, 10, 30, 27, 26, 27, 27, 78, 25, 24, 20, 21, 25, 177, 73, 68, 72, 72, 178, 71, 72, 69, 70, 181, 176, 69, 68, 66, 66, 65, 175, 429, 61, 40, 448, 44, 45, 51, 47, 420, 426, 173, 427, 425, 1062, 1072, 429, 428, 1071, 1067, 430, 165, 164, 426, 162

Offset

0,2

Comments

Up to n = 75, I have found no multiple > 12.

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Example

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.

Mathematica

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

Prog

(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]

Crossrefs

Sequence in context: A112953 A110139 A078146 * A227715 A173049 A272040

Adjacent sequences: A066833 A066834 A066835 * A066837 A066838 A066839

Keyword

nonn

Author

Robert G. Wilson v, Jan 20 2002

Status

approved