|
Search: id:A137997
|
|
|
| A137997 |
|
Numbers which are not the sum of a triangular number and zero or a prime = 3 (mod 4). |
|
+0
2
|
|
| 2, 5, 16, 27, 30, 42, 54, 61, 63, 90, 96, 129, 144, 165, 204, 216, 225, 285, 288, 309, 333, 340, 345, 390, 405, 423, 426, 448, 462, 525, 540, 556, 624, 651, 705, 801, 813, 876, 945, 960, 1056, 1230, 1371, 1380, 1470, 1491, 1827, 2085, 2157, 2181, 2220, 2355
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Zhi-Wei SUN conjectured that n=216 is the only number not of the form n = p + k(k+1)/2 with p a prime or zero, and more precisely that the numbers given in this sequence A137997(1..112) = 2,...,90441 are the only numbers which cannot be written in this form with p=0 or p=3 (mod 4).
|
|
LINKS
|
Zhi-Wei SUN, Post to the NMBRTHRY list
Zhi-Wei SUN, A new conjecture: n=p+x(x+1)/2, Mar 23, 2008.
|
|
PROGRAM
|
(PARI) { for( n=1, 10^8, t=sqrtint( 2*n ); if( 0>= p = n-t*(t+1)/2, !p & next, p -= t++ ); until( !t--, isprime( p+=t ) | next; p%4==3 & next(2)); print1( n", " ))}
|
|
CROSSREFS
|
Cf. A137996, A132399, A000040, A000217.
Sequence in context: A098048 A101847 A117557 this_sequence A139022 A053683 A082085
Adjacent sequences: A137994 A137995 A137996 this_sequence A137998 A137999 A138000
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
M. F. Hasler (www.univ-ag.fr/~mhasler), Mar 24 2008
|
|
|
Search completed in 0.002 seconds
|
