login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A228446 For odd n >= 5, lowest prime p such that n = p + x*(x+1) for some x > 0. 4

%I

%S 3,5,3,5,7,3,5,7,19,3,5,7,17,11,3,5,7,19,11,13,3,5,7,31,11,13,37,3,5,

%T 7,23,11,13,29,17,3,5,7,61,11,13,31,17,19,3,5,7,43,11,13,103,17,19,

%U 109,3,5,7,29,11,13,53,17,19,41,23,3,5,7,31,11,13,37

%N For odd n >= 5, lowest prime p such that n = p + x*(x+1) for some x > 0.

%C This is Sun's conjecture 1.4 in the paper listed below.

%C The plot shows an ever-widening band of sawtooth shape. New maxima values will include sequence members larger than the largest prime factor of the original n. An example is 19 encountered from n=21=3*7, 19>7.

%C a(A000124(n)) = 3; a(A133263(n)) = 5; a(A167614(n)) = 7. - _Reinhard Zumkeller_, Mar 12 2014

%D Z. W. Sun, On sums of primes and triangular numbers, Journal of Combinatorics and Number Theory 1(2009), no. 1, 65-76. (See Conjecture 1.4.)

%H T. D. Noe, <a href="/A228446/b228446.txt">Table of n, a(n) for n = 2..1000</a>

%H Z. W. Sun, <a href="http://arxiv.org/abs/0803.3737">On sums of primes and triangular numbers</a>, arXiv:0803.3737 [math.NT]

%e 21 = 19+1*2 where no solution exists using p = 2, 3, 5, 7, 11, 13, 17.

%e 51 = 31+4*5 where no lower odd prime provides a solution for odd 51.

%t nn = 14; ob = Table[n*(n+1), {n, nn}]; Table[p = Min[Select[n - ob, # > 0 && PrimeQ[#] &]]; p, {n, 5, ob[[-1]], 2}] (* _T. D. Noe_, Oct 27 2013 *)

%o (PARI) a(n) = {oddn = 2*n+1; x = oddn; while (! isprime(oddn - x*(x+1)), x--); oddn - x*(x+1);} \\ _Michel Marcus_, Oct 27 2013

%o (Haskell)

%o a228446 n = head

%o [q | let m = 2 * n + 1,

%o q <- map (m -) $ reverse $ takeWhile (< m) $ tail a002378_list,

%o a010051 q == 1]

%o -- _Reinhard Zumkeller_, Mar 12 2014

%Y Cf. A010051, A002378, A000217.

%K easy,nonn

%O 2,1

%A _Bill McEachen_, Oct 26 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)