

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
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OFFSET

2,1


COMMENTS

This is Sun's conjecture 1.4 in the paper listed below.
The plot shows an everwidening 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, 6576. (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 A253398
Adjacent sequences: A228443 A228444 A228445 * A228447 A228448 A228449


KEYWORD

easy,nonn


AUTHOR

Bill McEachen, Oct 26 2013


STATUS

approved



