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A090403
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Balanced primes: primes which are both the arithmetic mean and median of a sequence of 2k+1 consecutive primes, for some k.
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10
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5, 17, 29, 37, 53, 71, 79, 89, 137, 149, 151, 157, 173, 179, 193, 211, 227, 229, 257, 263, 281, 349, 353, 359, 373, 383, 397, 409, 419, 421, 433, 439, 487, 491, 563, 577, 593, 607, 631, 643, 653, 659, 677, 701, 709, 733, 751, 757, 787, 823, 827, 877, 947, 953
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All (2k+1)-balanced prime numbers, i.e.; a balanced prime of order k, is a prime such that p*(2k+1)=Sum_{i=n-k..n+k} p_i, where p_i being the i-th prime.
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EXAMPLE
| 17 is in the sequence because 17 = (7 + 11 + 13 + 17 + 19 + 23 + 29)/7, (k = 3) and
29 is in the sequence because 29 = (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)/15, (k = 7).
37 is a member because 37 = (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71)/17, 7&71 are eight primes away from 37.
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MATHEMATICA
| t[n_] := (For[k=1, !(SameQ[1/(2k+1)Sum[Prime[i], {i, n-k, n+k}], Prime[n]])&& k < n-1, k++ ]; k); b[n_] := If[t[n]<n-1||SameQ[1/(2n-1)Sum[Prime[i], {i, 2n-1}], Prime[n]], t[n], 0]; v={}; Do[If[b[n]!=0, v=Append[v, Prime[n]]], {n, 2, 168}]; v
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CROSSREFS
| Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704, A096711.
Sequence in context: A196142 A195032 A068829 * A096705 A023258 A030554
Adjacent sequences: A090400 A090401 A090402 * A090404 A090405 A090406
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KEYWORD
| easy,nonn
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AUTHOR
| Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Dec 07 2003
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EXTENSIONS
| Definition corrected by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 13 2006
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