login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Least positive integer that can be represented as the sum of a prime and a triangular number in exactly n ways.
2

%I #8 Aug 27 2012 11:47:02

%S 1,2,3,8,17,83,47,89,107,212,194,347,284,674,524,464,467,947,662,1187,

%T 1514,1304,1019,1229,1559,2189,1724,2699,2084,3434,2417,4022,3467,

%U 3824,3764,3362,5324,5879,5672,7214,5927,6179,6134,7079,6704,7727,10667

%N Least positive integer that can be represented as the sum of a prime and a triangular number in exactly n ways.

%H Donovan Johnson, <a href="/A101182/b101182.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = min{i such that i = A000040(j) + A000217(k) in n ways}.

%e a(0) = 1 because 1 is the smallest positive integer that cannot be represented as sum of a prime and a triangular number (since 2 is the smallest prime).

%e a(1) = 2 = 2 + 0; a(2) = 3 = 3 + 0 = 2 + 1; a(3) = 8 = 2 + 6 = 5 + 3 = 7 + 1.

%Y Cf. A000040, A000217, A076768.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_ and _Ray Chandler_, Dec 14 2004