A138363 -id:A138363 - cp's OEIS frontend

A074267 Primes of form p^n + k, where p is prime, n>1 and 0

5, 11, 17, 29, 53, 83, 127, 131, 173, 179, 181, 257, 293, 347, 349, 367, 373, 379, 541, 547, 853, 857, 859, 863, 967, 971, 977, 983, 991, 1373, 1381, 1399, 1693, 1697, 1699, 1709, 1721, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 2203, 2207, 2213, 2221, 2237

Offset: 1

Reinhard Zumkeller, Sep 20 2002

The representation is not unique: a(7)=127=5^3+2=11^2+5.

A138363(A049084(a(n))) > 0.

R. Zumkeller, Table of n, a(n) for n = 1..1000

lst = {}; Do[q = p^n + k; If[ PrimeQ@p && PrimeQ@q, AppendTo[lst, q]], {p, 2, 50}, {k, p - 1}, {n, 2, Log[p, 3000]}]; Take[ Union@ lst, 49] (* Robert G. Wilson v, Sep 22 2007 *)

A136335 Indices of the primes p for which the number of representations of p as the sum of a perfect prime power (A025475: q^e with e>1) and an integer k which is less than q exceeds one.

Original entry on oeis.org

10, 31, 14774, 14775, 65686, 110128, 110129, 110130, 110131, 110132, 110133, 110134, 110135, 110136, 110137, 165952, 165953, 165954, 165955, 165956, 165957, 165958, 304841, 304842, 304843, 304844, 304845, 304846, 304847

Offset: 1

Reinhard Zumkeller & Robert G. Wilson v, Mar 23 2008

nonn

Where A138363 exceeds 1.

			A000040(10)=29; A138363(10) = #{4+5^2, 2+3^3} = 2.

Cf. A138363, A074267.

f[n_] := Block[{c = 0, e, j, k = 1, p = Prime@n, q}, j = 1 + PrimePi@ Sqrt@ p; While[k < j, q = Prime@k; If[p < q + q^Floor@ Log[q, p], c++ ]; k++ ]; c]; lst = {}; Do[ If[f@n > 1, AppendTo[lst, n]; Print[Prime@n]], {n, 25*10^5}]

cp's OEIS Frontend

A074267 Primes of form p^n + k, where p is prime, n>1 and 0

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