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

0,2

Comments

Note that A002471 allows for k to equal zero.

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

Example

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.

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

Crossrefs

Cf. A002471.

Sequence in context: A147118 A147157 A146826 * A250223 A250271 A289842

Adjacent sequences: A059397 A059398 A059399 * A059401 A059402 A059403

Keyword

nonn

Author

Robert G. Wilson v, Mar 15 2001

Extensions

Name clarified by Donovan Johnson, Nov 24 2012

Status

approved