A086534 Smallest prime p sandwiched between two numbers that are divisible by n-th powers.

2, 17, 271, 1249, 13121, 13121, 153089, 1272833, 28146689, 193562623, 652963841, 1378557953, 29096394751, 316431663103, 2191221587969, 15356401156097, 128200797454337, 314394051346433, 314394051346433, 28344942091829249, 201993039632138239, 267803891553271807

Offset

1,1

Comments

Conjecture: sequence is finite.

Links

Table of n, a(n) for n=1..22.

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: A301584 A195443 A176585 * A198287 A338635 A268705

Adjacent sequences: A086531 A086532 A086533 * A086535 A086536 A086537

Keyword

nonn

Author

Amarnath Murthy, Aug 17 2003

Extensions

Edited and extended by Robert G. Wilson v, Aug 18 2003

a(5) corrected. a(13)-a(22) from Donovan Johnson, Sep 02 2008

Status

approved