|
| |
|
|
A360930
|
|
Odd numbers which cannot be expressed as p + q*(q-1) where p and q are primes.
|
|
2
|
|
|
|
1, 3, 41, 97, 135, 251, 255, 341, 363, 377, 405, 671, 737, 765, 1007, 1049, 1287, 1371, 1377, 1427, 1605, 1697, 1745, 1805, 2067, 2177, 2201, 2277, 2333, 2477, 2657, 2711, 3077, 3101, 3117, 3149, 3191, 3437, 3557, 3597, 3611, 3983, 4647, 4787, 4797, 5117
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
It is conjectured that 772277 is the largest odd integer which cannot be expressed as p + q*(q-1) where p and q are primes.
q*(q-1) is even which implies that p must be an odd prime.
The expression p + q*(q-1) resembles the expression p + 2*q used in Lemoine's conjecture.
|
|
|
LINKS
|
|
|
|
MATHEMATICA
|
a[1]=1; a[n_]:=a[n]=(k=a[n-1]; c=True; While[c, k=k+2; c=False; q=2; While[!c&&q*(q-1)<k, p=k-(q*(q-1)); c=PrimeQ[p]; q=NextPrime[q]]]; k); Table[a[n], {n, 1, 150}]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
