|
| |
|
|
A075408
|
|
Perfect powers pp such that pp+1 is prime.
|
|
0
| |
|
|
1, 4, 16, 36, 100, 196, 256, 400, 576, 676, 1296, 1600, 2916, 3136, 4356, 5476, 7056, 8100, 8836, 12100, 13456, 14400, 15376, 15876, 16900, 17956, 21316, 22500, 24336, 25600, 28900, 30976, 32400, 33856, 41616, 42436, 44100, 50176, 52900, 55696
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Of 1110 pp's < 10^6, 112 are such that pp+1 is prime and only seven are such that pp-1 is prime (see Mersenne primes (A000668)).
|
|
|
EXAMPLE
| pp=324900 is OK because pp=570^2 and pp+1=324901 (prime).
|
|
|
MATHEMATICA
| pp = Join[ Select[ Range[56000], Apply[GCD, Last[ Transpose[ FactorInteger[ # ]]]] > 1 & ]]; Select[pp, PrimeQ[ # + 1] & ]
|
|
|
CROSSREFS
| Equals A002496(n) - 1.
Cf. A001597: perfect powers, m^k where m is an integer and k >= 2. A075398, perfect powers pp such that pp-1 is prime.
Sequence in context: A207069 A189145 A005722 * A206981 A181795 A136404
Adjacent sequences: A075405 A075406 A075407 * A075409 A075410 A075411
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Oct 11 2002
|
|
|
EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 14 2002
Edited by N. J. A. Sloane, Dec 17 2009 at the suggestion of Rick Shepherd
|
| |
|
|
