|
| |
|
|
A075127
|
|
Safe perfect powers: perfect powers n such that (n-1)/2 is also a perfect power.
|
|
1
| |
|
|
9, 243, 289, 9801, 332929, 11309769, 384199201, 13051463049, 443365544449, 15061377048201, 511643454094369, 17380816062160329, 590436102659356801, 20057446674355970889, 681362750825443653409
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| If both powers are squares, the smaller square is a triangular number, and all square triangular numbers (A0011110) correspond to a member in this sequence. This proves that this sequence is infinite. Are there only finitely many other members, i.e., is A075127 \ A055792 finite? [From Charles R Greathouse IV, Dec 12 2010]
|
|
|
MATHEMATICA
| pp = Select[ Range[10^8], Apply[ GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]; Select[pp, Apply[GCD, Last[ Transpose[ FactorInteger[( # - 1)/2]]]] > 1 & ]
|
|
|
CROSSREFS
| Cf. A001597, A070428, A075114, A055792, A001110.
Sequence in context: A157569 A085799 A183903 * A013733 A167005 A112028
Adjacent sequences: A075124 A075125 A075126 * A075128 A075129 A075130
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Oct 11 2002
|
|
|
EXTENSIONS
| One more term from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 16 2002
a(7)-a(15) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Mar 10 2010
|
| |
|
|
