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A096695 Least balanced prime (A090403) of index n (A096693). 6
2, 5, 211, 53, 157, 173, 304517 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..6.

EXAMPLE

a(1) = 5 because 5 = (3 + 5 + 7)/3.

a(2) = 211 because 211 = (199 + 211 + 223)/3

= (179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239 + 241)/13.

a(3) = 53 because 53 = (47 + 53 + 59)/3 = (41 + 43 + 47 + 53 + 59 + 61 + 67)/7

= (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)/11.

a(4) = 157 because 157 = (151 + 157 + 163)/3 = (139 + 149 + 151 + 157 + 163 + 167 + 173)/7

= (131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181)/11

= (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)/25.

a(5) = 173 because 173 = (167 + 173 + 179)/3 = (157 + 163 + 167 + 173 + 179 + 181 + 191)/7

= (131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223)/17

= (109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233)/23

= (107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239)/25.

a(6) = 304517 because 304517 = (304511 + 304517 + 304523)/3

= (304489 + 304501 + 304511 + 304517 + 304523 + 304537 + 304541)/7

= (304481 + 304489 + 304501 + 304511 + 304517 + 304523 + 304537 + 304541 + 304553)/9

= (303691 + ... + 304517 + ... + 305339)/135 = (303649 + ... + 304517 + ... + 305369)/143

MATHEMATICA

f[n_] := Block[{c = 0, k = 1, p = Prime[n], s = Plus @@ Table[ Prime[i], {i, n - 1, n + 1}]}, While[k != n - 1, If[s == (2k + 1)p, c++ ]; k++; s = s + Prime[n - k] + Prime[n + k]]; c]; t = Table[0, {15}]; Do[a = f[n]; If[a < 50 && t[[a + 1]] == 0, t[[a + 1]] = Prime[n]; Print[a + 1, " = ", Prime[n]]], {n, 32000}]; t

CROSSREFS

Cf. A096693, A096705, A096706, A096707, A096708, A096709.

Sequence in context: A013105 A208210 A216458 * A084297 A041873 A072118

Adjacent sequences:  A096692 A096693 A096694 * A096696 A096697 A096698

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jun 26 2004

STATUS

approved

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Last modified February 18 09:28 EST 2019. Contains 320249 sequences. (Running on oeis4.)