This site is supported by donations to The OEIS Foundation. 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
 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, 7, 23, 11, 13, 29, 17, 3, 5, 7, 61, 11, 13, 31, 17, 19, 3, 5, 7, 43, 11, 13, 103, 17, 19, 109, 3, 5, 7, 29, 11, 13, 53, 17, 19, 41, 23, 3, 5, 7, 31, 11, 13, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS This is Sun's conjecture 1.4 in the paper listed below. 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. a(A000124(n)) = 3; a(A133263(n)) = 5; a(A167614(n)) = 7. - Reinhard Zumkeller, Mar 12 2014 REFERENCES 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.) LINKS T. D. Noe, Table of n, a(n) for n = 2..1000 Z. W. Sun, On sums of primes and triangular numbers, arXiv:0803.3737 [math.NT] EXAMPLE 21 = 19+1*2  where no solution exists using p = 2, 3, 5, 7, 11, 13, 17. 51 = 31+4*5  where no lower odd prime provides a solution for odd 51. MATHEMATICA 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 *) PROG (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 (Haskell) a228446 n = head    [q | let m = 2 * n + 1,         q <- map (m -) \$ reverse \$ takeWhile (< m) \$ tail a002378_list,         a010051 q == 1] -- Reinhard Zumkeller, Mar 12 2014 CROSSREFS Cf. A010051, A002378, A000217. Sequence in context: A121795 A253027 A249384 * A188889 A219604 A296489 Adjacent sequences:  A228443 A228444 A228445 * A228447 A228448 A228449 KEYWORD easy,nonn AUTHOR Bill McEachen, Oct 26 2013 STATUS approved

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.

Last modified November 22 18:55 EST 2019. Contains 329410 sequences. (Running on oeis4.)