A059400 a(n) is the least odd number of the form p + k^2 with p prime and k > 0 which can be represented in exactly n different ways.
1, 3, 11, 27, 77, 83, 167, 293, 227, 503, 437, 887, 923, 1007, 1133, 1487, 2243, 2147, 2477, 2273, 2537, 3167, 3947, 4457, 4703, 3737, 3713, 5843, 6233, 8123, 8333, 5297, 11513, 10127, 9407, 10853, 10577, 13187, 8153, 12473, 8777, 15923, 16463, 17513
Offset: 0
Keywords
Examples
a(3) = 27 because 27 = 23+2^2 = 11+4^2 = 2+5^2 and is the least odd number to exhibit this property of 3 representations.
References
- David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, 1997, page 63.
Links
- Donovan Johnson, Table of n, a(n) for n = 0..1000
Crossrefs
Cf. A002471.
Programs
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Mathematica
a = Table[ 0, {55} ]; Do[ c = 0; k = 1; While[ n - k^2 > 1, If[ PrimeQ[ n - k^2], c++ ]; k++ ]; If[ a[[c]] == 0, a[[c]] = n], { n, 1, 30500, 2} ]; a
Extensions
Name clarified by Donovan Johnson, Nov 24 2012
Comments