A102821 -id:A102821 - cp's OEIS frontend

A104492 Cube excess of the n-th prime.

1, 2, 4, 6, 3, 5, 9, 11, 15, 2, 4, 10, 14, 16, 20, 26, 32, 34, 3, 7, 9, 15, 19, 25, 33, 37, 39, 43, 45, 49, 2, 6, 12, 14, 24, 26, 32, 38, 42, 48, 54, 56, 66, 68, 72, 74, 86, 7, 11, 13, 17, 23, 25, 35, 41, 47, 53, 55, 61, 65, 67, 77, 91, 95, 97, 101, 115, 121, 4, 6, 10, 16, 24, 30

Offset: 1

Jonathan Vos Post, Mar 10 2005

			a(48) = 7 because the 48th prime is 223 and 223 - 6^3 = 7, while 223 - 7^3 = -120.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A053186, A055400, A056892, A102821.

lst={};Do[p=Prime[n];s=p^(1/3);f=Floor[s];a=f^3;d=p-a;AppendTo[lst,d],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)
#-Floor[Surd[#,3]]^3&/@Prime[Range[80]] (* Harvey P. Dale, Feb 15 2018 *)

a(n) = A055400(A000040(n)).

a(n) = prime(n) - floor(prime(n)^(1/3))^3. - Jon E. Schoenfield, Jan 17 2015

A104491 Prime numbers n for which the square excess of the n-th prime is prime.

Original entry on oeis.org

2, 5, 13, 19, 23, 37, 67, 71, 83, 107, 109, 113, 139, 157, 173, 199, 271

Offset: 1

Jonathan Vos Post, Mar 10 2005

			199 is an element of this sequence because 199 is prime and the 199th prime is 1217 and 1217 - 34^2 = 61 and 61 is prime, while 1217 - 35^2 = -8.

Cf. A000040, A053186, A102821.

n such that A102821(n) is prime. n such that A053186(A000040(n)) is an element of A000040.

A104493 Numbers n for which the cube excess of the n-th prime is prime.

Original entry on oeis.org

2, 5, 6, 8, 10, 19, 20, 23, 26, 28, 31, 48, 49, 50, 51, 52, 55, 56, 57, 59, 61, 65, 66, 99, 100, 105, 110, 112, 114, 117, 121, 125, 127, 170, 171, 173, 178, 184, 185, 186, 190, 192, 194, 196, 200, 201, 206, 208, 214, 270, 271, 272, 274, 277, 278, 279, 280, 282

Offset: 1

Jonathan Vos Post, Mar 19 2005

			99 is an element of this sequence because the 99th prime is 523, 523 - 8^3 = 523-512 = 11 and 11 is prime. 100 is in this sequence because the 100th prime is 541 and 541-8^3 = 29, which is prime.

Cf. A000040, A053186, A055400, A056892, A102821, A104492.

f[n_] := Block[{k = 1, p = Prime[n]}, While[k^3 < p, k++ ]; p - (k - 1)^3]; Select[ Range[ 284], PrimeQ[ f[ # ]] &] (* Robert G. Wilson v, Mar 19 2005 *)

n such that A055400(A000040(n)) is an element of A000040. n such that A104492(n) is prime.

More terms from Robert G. Wilson v, Mar 19 2005

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A104492 Cube excess of the n-th prime.

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A104491 Prime numbers n for which the square excess of the n-th prime is prime.

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A104493 Numbers n for which the cube excess of the n-th prime is prime.

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