A081506
Primes of the form 2^k + 3^k + 4^k.
Original entry on oeis.org
3, 29, 353, 4889, 72353, 105312291668560568089831550410013687058921146068446092937783402353
Offset: 1
k = 2: 2^2 + 3^2 + 4^2 = 4 + 9 + 16 = 29, which is prime.
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Do[s=2^w+3^w+4^w; If[IntegerQ[w/100], Print[{w}]]; If[PrimeQ[s], Print[{w, s}]], {w, 0, 1000}]
Select[Table[2^n+3^n+4^n,{n,0,200}],PrimeQ] (* Harvey P. Dale, Aug 20 2015 *)
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lista(kmax) = {my(p); for(k = 0, kmax, p = 2^k + 3^k + 4^k; if(isprime(p), print1(p, ", ")));} \\ Amiram Eldar, Aug 17 2024
A137786
a(n) = 4^n - 3^n - 2^n.
Original entry on oeis.org
-1, -1, 3, 29, 159, 749, 3303, 14069, 58719, 241949, 988503, 4015109, 16241679, 65506349, 263636103, 1059360149, 4251855039, 17050597949, 68331794103, 273715121189, 1096023794799, 4387584060749, 17560800790503, 70274592610229, 281192530396959, 1125052584678749
Offset: 0
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I:=[-1,-1,3]; [n le 3 select I[n] else 9*Self(n-1)-26*Self(n-2)+24*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 12 2014
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A137786:=n->4^n - 3^n - 2^n; seq(A137786(n), n=0..25); # Wesley Ivan Hurt, Feb 10 2014
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Table[4^n - 3^n - 2^n, {n, 0, 25}] (* Bruno Berselli, Jul 04 2012 *)
LinearRecurrence[{9,-26,24},{-1,-1,3},30] (* Harvey P. Dale, Sep 19 2012 *)
CoefficientList[Series[-(1 - 8 x + 14 x^2)/((1 - 2 x) (1 - 3 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *)
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a(n) = 4^n-3^n-2^n; \\ Joerg Arndt, Jul 04 2012
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print([4**n - 3**n - 2**n for n in range(99)])
# Alex Ratushnyak, Jul 03 2012
Offset set to 0, terms corrected, more terms added by
Alex Ratushnyak, Jul 03 2012.
A299145
Primes of the form j^k + (j-1)^k + ... + 2^k, for j > 1 and k > 0.
Original entry on oeis.org
2, 5, 13, 29, 97, 139, 353, 4889, 72353, 353815699, 42065402653, 84998999651, 102769130749, 15622297824266188673, 28101527071305611527, 20896779938941631284493075599148668795944697935466419104293, 105312291668560568089831550410013687058921146068446092937783402353
Offset: 1
2 = 2^1;
5 = 3^1 + 2^1;
13 = 3^2 + 2^2;
29 = 4^2 + 3^2 + 2^2;
97 = 3^4 + 2^4;
139 = 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2;
353 = 4^4 + 3^4 + 2^4;
4889 = 4^6 + 3^6 + 2^6;
72353 = 4^8 + 3^8 + 2^8;
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With[{nn = 350}, Sort@ Flatten@ Map[Select[#, PrimeQ] &, Table[Total[Range[j, 1, -1]^k] - 1, {j, 2, nn}, {k, nn - j}]]] (* Michael De Vlieger, Feb 03 2018 *)
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limit=100000; v=vector(limit); for(n=1, ceil((-1+(1+8*limit)^(1/2))/2), for(k=1, logint(limit, n+0^(n-1)), a=sum(i=1,n,i^k)-1;if(isprime(a)&&a
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