|
| |
|
|
A086534
|
|
Smallest prime p sandwiched between two numbers that are divisible by n-th powers.
|
|
0
| |
|
|
2, 17, 271, 1249, 13121, 13121, 153089, 1272833, 28146689, 193562623, 652963841, 1378557953, 29096394751, 316431663103, 2191221587969, 15356401156097, 128200797454337, 314394051346433, 314394051346433, 28344942091829249, 201993039632138239, 267803891553271807
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Conjecture: sequence is finite.
|
|
|
EXAMPLE
| a(3) = 271, 270 = 3^3*10 and 272 = 2^3*34. 271 is the smallest such number.
a(4) = 1249, 1248 =2^4*78, 1250 = 5^4*2. 1250 is the smallest such number.
|
|
|
MATHEMATICA
| PrimeExponents[n_] := Max[ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[n]]]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = Table[0, {15}]; p = 1; Do[p = NextPrim[p]; b = Min[ PrimeExponents[p - 1], PrimeExponents[p + 1]]; If[ a[[b]] == 0, a[[b]] = p; Print[b, " ", p]], {n, 1, 70000000}]; a
|
|
|
CROSSREFS
| Cf. A086708, A086709.
Sequence in context: A099714 A195443 A176585 * A198287 A078367 A090306
Adjacent sequences: A086531 A086532 A086533 * A086535 A086536 A086537
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 17 2003
|
|
|
EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 18 2003
a(5) corrected. a(13)-a(22) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 02 2008
|
| |
|
|
