|
|
A247011
|
|
Numbers n for which A242719(n) = (prime(n) + 2)^2 + 1.
|
|
5
|
|
|
5, 7, 13, 17, 26, 33, 64, 81, 98, 140, 171, 176, 190, 201, 215, 225, 318, 332, 336, 444, 469, 475, 495, 551, 558, 563, 577, 601, 636, 671, 828, 849, 862, 870, 948, 1004, 1064, 1074, 1189, 1198, 1230, 1238, 1305, 1328, 1445, 1449, 1528, 1618, 1634, 1642, 1679
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
(prime(n) + 2)^2 + 1 is the second minimal possible value of A242719(n) after prime(n)^2 + 1. Indeed, by the definition lpf(A242719(n) - 3) > lpf(A242719(n) - 1) >= prime(n), thus after prime(n)^2 + 1 we should consider prime(n)*(prime(n) + 2) + 1. Then prime(n) should be lesser number of twin primes, but then prime(n) + 1 == 0 (mod 3). So, prime(n)*(prime(n) + 2) - 2 == 0 (mod 3). Analogously one can prove that prime(n)*(prime(n) + 4) - 2 == 0 (mod 3).
Note that for the sequence prime(n+1) is in intersection of A006512 and A062326, but prime(n) is not in A062326.
|
|
LINKS
|
|
|
FORMULA
|
Intersection of A247011 and A246824 forms sequence 81, 215, 828, 1189, 1634, ... For these values of n we have A242719(n) - A242720(n) = 2*(prime(n) + 1).
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|