cp's OEIS Frontend

A095841 Prime powers having exactly one partition into two prime powers.

%I A095841 #21 Mar 04 2019 18:44:07
%S A095841 2,3,127,163,179,191,193,223,239,251,269,311,337,343,389,419,431,457,
%T A095841 491,547,557,569,599,613,653,659,673,683,719,739,787,821,839,853,883,
%U A095841 911,929,953,967,977,1117,1123,1201,1229,1249,1283,1289,1297,1303,1327,1381,1409,1423,1439,1451,1471,1481,1499,1607,1663,1681
%N A095841 Prime powers having exactly one partition into two prime powers.
%C A095841 A095840(A095874(a(n))) = 1.
%C A095841 A071330(a(n)) = 1.
%H A095841 Reinhard Zumkeller, <a href="/A095841/b095841.txt">Table of n, a(n) for n = 1..10000</a>
%p A095841 N:= 10^4: # to get all terms <= N
%p A095841 primepows:= {1,seq(seq(p^n, n=1..floor(log[p](N))),
%p A095841     p=select(isprime,[2,seq(2*k+1,k=1..(N-1)/2)]))}:
%p A095841 npp:= nops(primepows):
%p A095841 B:= Vector(N,datatype=integer[4]):
%p A095841 for n from 1 to npp do for m from n to npp do
%p A095841    j:= primepows[n]+primepows[m];
%p A095841    if j <= N then B[j]:= B[j]+1 fi;
%p A095841 od od:
%p A095841 select(t -> B[t] = 1, primepows); # _Robert Israel_, Nov 21 2014
%t A095841 max = 2000; ppQ[n_] := n == 1 || PrimePowerQ[n]; pp = Select[Range[max], ppQ]; lp = Length[pp]; Table[pp[[i]] + pp[[j]], {i, 1, lp}, {j, i, lp}] // Flatten // Select[#, ppQ[#] && # <= max&]& // Sort // Split // Select[#, Length[#] == 1&]& // Flatten (* _Jean-François Alcover_, Mar 04 2019 *)
%o A095841 (Haskell)
%o A095841 a095841 n = a095841_list !! (n-1)
%o A095841 a095841_list = filter ((== 1) . a071330) a000961_list
%o A095841 -- _Reinhard Zumkeller_, Jan 11 2013
%o A095841 (PARI) is(n)=if(n<127,return(n==2||n==3)); isprimepower(n) && sum(i=2,n\2,isprimepower(i)&&isprimepower(n-i))==1 \\ naive; _Charles R Greathouse IV_, Nov 21 2014
%o A095841 (PARI) is(n)=if(!isprimepower(n), return(0)); my(s); forprime(p=2, n\2, if(isprimepower(n-p) && s++>1, return(0))); for(e=2, log(n)\log(2), forprime(p=2, sqrtnint(n\2, e), if(isprimepower(n-p^e) && s++>1, return(0)))); s+(!!isprimepower(n-1))==1 || n==2 \\ faster; _Charles R Greathouse IV_, Nov 21 2014
%o A095841 (PARI) has(n)=my(s); forprime(p=2, n\2, if(isprimepower(n-p) && s++>1, return(0))); for(e=2, log(n)\log(2), forprime(p=2, sqrtnint(n\2, e), if(isprimepower(n-p^e) && s++>1, return(0)))); s+(!!isprimepower(n-1))==1
%o A095841 list(lim)=my(v=List([2])); forprime(p=2,lim,if(has(p), listput(v,p))); for(e=2,log(lim)\log(2), forprime(p=2,lim^(1/e), if(has(p^e), listput(v,p^e)))); Set(v) \\ _Charles R Greathouse IV_, Nov 21 2014
%Y A095841 Cf. A000961, A095842.
%Y A095841 Intersection of A208247 and A000961.
%Y A095841 Cf. A071330, A095840, A095874.
%K A095841 nonn
%O A095841 1,1
%A A095841 _Reinhard Zumkeller_, Jun 10 2004