

A226133


Integers of the form (pq1)/24 where p < q are primes.


1



6, 9, 11, 20, 21, 23, 27, 29, 30, 31, 33, 34, 36, 37, 38, 41, 44, 45, 49, 53, 56, 58, 59, 60, 61, 63, 64, 65, 66, 68, 79, 80, 81, 82, 85, 94, 96, 97, 98, 102, 104, 106, 107, 110, 115, 116, 120, 122, 124, 128, 129
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OFFSET

1,1


COMMENTS

Results for p = q are given in A024702, which is complementary.
All integer results when viewed in the triangle occur in loosely diagonal, interrupted "bands" roughly (or exactly) parallel to main diagonal, such that q  p = 24m, where m = 1 for the first band closest to the main diagonal, m = 2 for the second band, m = 3 for the third band, etc. The main diagonal p = q can be considered as fitting in this pattern where m = 0.
A general "rule" can be stated: If qp = 24m for any m >= 0 and primes p < q, then pq1 is divisible by 24. This follows algebraically from the know "rule" that p^2 1 is divisible by 24 for any prime p > 3 as given in A024702.
No result will occur twice, even when including A024702, because the product of any two primes is unique within the set.
Integer results have a density of about 12% to 13% for all possible p,q pairs among the first few hundred primes.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

(5*291)/24 = 6, (7*311)/24 = 9, (5*531)/24 = 11, also note about these three examples, in order, that 295 = 24, 317 = 24 and 535 = 48.


PROG

(PARI) is(n)=my(f=factor(24*n+1)); #f[, 1]==2&&f[1, 2]==1&&f[2, 2]==1 \\ Charles R Greathouse IV, May 30 2013


CROSSREFS

Complementary to A024702.
Sequence in context: A275274 A131834 A084418 * A125971 A322158 A143710
Adjacent sequences: A226130 A226131 A226132 * A226134 A226135 A226136


KEYWORD

nonn


AUTHOR

Richard R. Forberg, May 27 2013


EXTENSIONS

Missing a(8) from Charles R Greathouse IV, May 31 2013


STATUS

approved



