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%I #11 Jan 25 2021 10:49:13
%S 2,79,1217,2879,7121,152879,178897,12781103,24233953,25553183,
%T 29147633,70852367,1800921329,3205490207,6270364129,30533756207,
%U 39265770209,52240479791,68933130209,73192853807,74570506193,78996293183
%N a(1) = 2; a(n) is the smallest prime > a(n-1) such that a(n) + a(n-1) is a fourth power.
%C Cf. similar sequences A062064, A062066.
%e 2+79=3^4, 79+1217=6^4, etc.
%t a=2;s={a};Do[p=n^4-a;If[p>a&&PrimeQ[p],AppendTo[s,p];a=p],{n,2,3000}];s
%t sp4p[n_]:=Module[{k=NextPrime[n]},While[!IntegerQ[Surd[n+k,4]],k = NextPrime[ k]];k]; NestList[sp4p,2,21] (* _Harvey P. Dale_, Apr 02 2018 *)
%o (PARI) print1(s=a=2); for(n=1,99,until(isprime(s++^4-a),);print1(", "a=s^4-a)) \\ _M. F. Hasler_, Oct 03 2010
%Y Cf. A062064, A062066.
%K nonn
%O 1,1
%A _Zak Seidov_, Jan 04 2006
%E Edited by _Zak Seidov_, Sep 28 2010, Oct 03 2010
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