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Search: id:A086534
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| A086534 |
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Smallest prime p sandwiched between two numbers that are divisible by n-th powers. |
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+0
1
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| 2, 17, 271, 1249, 13121, 13121, 153089, 1272833, 28146689, 193562623, 652963841, 1378557953, 29096394751, 316431663103, 2191221587969, 15356401156097, 128200797454337, 314394051346433, 314394051346433, 28344942091829249
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: sequence is finite.
a(21) = 201993039632138239. a(22) = 267803891553271807. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 02 2008]
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EXAMPLE
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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.
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MATHEMATICA
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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
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CROSSREFS
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Cf. A086708, A086709.
Adjacent sequences: A086531 A086532 A086533 this_sequence A086535 A086536 A086537
Sequence in context: A029735 A037896 A099714 this_sequence A078367 A090306 A007785
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 17 2003
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EXTENSIONS
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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
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