A059400 - OEIS

%I #9 Nov 25 2012 02:31:45

%S 1,3,11,27,77,83,167,293,227,503,437,887,923,1007,1133,1487,2243,2147,

%T 2477,2273,2537,3167,3947,4457,4703,3737,3713,5843,6233,8123,8333,

%U 5297,11513,10127,9407,10853,10577,13187,8153,12473,8777,15923,16463,17513

%N 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.

%C Note that A002471 allows for k to equal zero.

%D David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, 1997, page 63.

%H Donovan Johnson, <a href="/A059400/b059400.txt">Table of n, a(n) for n = 0..1000</a>

%e 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.

%t 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

%Y Cf. A002471.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Mar 15 2001

%E Name clarified by _Donovan Johnson_, Nov 24 2012