A099228
Primes of the form m^k-k, with m and k > 1.
Original entry on oeis.org
2, 5, 7, 23, 47, 61, 79, 167, 223, 359, 439, 503, 509, 727, 839, 997, 1019, 1087, 1223, 1367, 1847, 2207, 2399, 2741, 3023, 3719, 3967, 4093, 4759, 5039, 5623, 5927, 6553, 7919, 8179, 8647, 10607, 11447, 13687, 14159, 14639, 15619, 16127, 17159, 17573
Offset: 1
Cf.
A057897 (numbers of the form m^k-k, with m and k > 1),
A084746 (least k such that n^k-k is prime).
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nLim=32000; lst={}; Do[k=2; While[n=m^k-k; n<=nLim, AppendTo[lst, n]; k++ ], {m, 2, Sqrt[nLim]}]; Select[Union[lst], PrimeQ]
A178327
Numbers k such that k^p+p is prime, where p is product of the digits of k.
Original entry on oeis.org
1, 21, 6617, 12131, 12441, 114917, 121221, 124281, 125121, 145581, 172631, 182121, 191213, 211551, 221211, 221421, 241213, 293143, 421531, 421821
Offset: 1
21^(2*1)+(2*1) is prime so 21 is a term.
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Do[p=Apply[Times, IntegerDigits[n]]; If[PrimeQ[n^p+p], Print[n]],
{n, 1, 27501, 2}]
A344990
Primes of the form m^k +- k, with m,k > 1.
Original entry on oeis.org
2, 5, 7, 11, 23, 37, 47, 61, 67, 79, 83, 167, 223, 227, 359, 439, 443, 503, 509, 521, 727, 839, 997, 1019, 1087, 1091, 1223, 1367, 1523, 1847, 2027, 2207, 2399, 2741, 3023, 3251, 3719, 3967, 4093, 4099, 4759, 5039, 5623, 5927, 6553, 6563, 6569, 7919, 8179
Offset: 1
2 = 2^2 - 2,
5 = 2^3 - 3,
7 = 3^2 - 2,
11 = 3^2 + 2,
23 = 5^2 - 2,
37 = 2^5 + 5,
47 = 7^2 - 2,
61 = 4^3 - 3,
67 = 4^3 + 3,
79 = 9^2 - 2,
83 = 9^2 + 2,
167 = 13^2 - 2,
223 = 15^2 - 2,
227 = 15^2 + 2,
359 = 19^2 - 2,
439 = 21^2 - 2,
443 = 21^2 + 2,
503 = 2^9 - 9,
509 = 8^3 - 3,
521 = 2^9 + 9,
...
Showing 1-3 of 3 results.
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