A145446 -id:A145446 - cp's OEIS frontend

A145449 Numbers n such that A145445(n) = A145446(n).

16, 17, 18, 123, 124, 125, 126, 127, 128, 129, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 1797, 1798, 1799, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818

Offset: 1

Zak Seidov, Oct 10 2008

nonn

Numbers n such that s(n), the smallest square > n-th prime, equals q(n), the smallest cube > n-th prime, s(n) = A145445(n), q(n) = A145446(n).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

A104103, A104147, A145445, A145446, A145447

Do[If[Ceiling[Prime[n]^(1/3)]^3 == Ceiling[Prime[n]^(1/2)]^2,Print[n]],{n,10000}]

A145447 a(n) = the smallest square (and/or cube) > n-th prime.

Original entry on oeis.org

4, 4, 8, 8, 16, 16, 25, 25, 25, 36, 36, 49, 49, 49, 49, 64, 64, 64, 81, 81, 81, 81, 100, 100, 100, 121, 121, 121, 121, 121, 144, 144, 144, 144, 169, 169, 169, 169, 169, 196, 196, 196, 196, 196, 216, 216, 216, 225, 256, 256, 256, 256, 256, 256, 289, 289, 289, 289

Offset: 1

Zak Seidov, Oct 10 2008

nonn

a(n) = min(A145445(n), A145446(n) )= min ([A104103(n)]^2, [A104147(n)]^3)

A104103, A104147, A145445, A145446

Table[Min[{Ceiling[Prime[n]^(1/3)]^3,Ceiling[Prime[n]^(1/2)]^2}],{n,100}]

A163849 Primes p such that the difference between the nearest cubes above and below p is prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 733, 739, 743, 751, 757, 761, 769, 773

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 05 2009

There is a sequence A048763(A000040(n)) = A145446(n) of nearest cubes above the primes and a sequence A048762(A000040(n)) of nearest cubes below the primes.

If the difference A145446(n) - A048762(A000040(n)) is prime, then A000040(n) is in this sequence.

			The difference of cubes 6^3 - 5^3 = 91 = 7*13 is not prime, so the primes larger than 5^3 = 125 but smaller than 6^3 = 216 are not in the sequence.

G. C. Greubel, Table of n, a(n) for n = 1..2500

Cf. A111252, A145446.

f[n_]:=IntegerPart[n^(1/3)]; lst={};Do[p=Prime[n];If[PrimeQ[(f[p]+1)^3-f[p]^3], AppendTo[lst,p]],{n,6!}];lst

Edited by R. J. Mathar, Aug 12 2009

cp's OEIS Frontend

A145449 Numbers n such that A145445(n) = A145446(n).

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A145447 a(n) = the smallest square (and/or cube) > n-th prime.

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Author

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Crossrefs

Programs

Mathematica

A163849 Primes p such that the difference between the nearest cubes above and below p is prime.

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Mathematica

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