|
%I #7 Oct 15 2013 22:31:57
%S 103,457,1009,1663,2953,3079,6043,12007,17707,20749,21499,25579,28537,
%T 30703,41227,54367,55663,59443,66973,70309,81547,83557,90019,97003,
%U 101359,102559,105367,108499,116239,120847,126019,129733,133873,138403
%N Primes p(x) satisfying the following conditions: [1]# A082882(x)=1; [2]# {p(x),p(x+1)} are not twin primes; [3]# values of A075860(j) for j composites between these two non-twin primes are identical. See also A075860, A082880-A082882.
%e p[2033]=17007 is here because next prime is 17013;
%e for the five j inter-prime composites
%e i.e. if j is from {17008,..,17012} the values
%e of A075860 are identical: {7,7,7,7,7}, so A082882(2033)=1;
%e Smallest such example is a(1)=103 with this sophisticated
%e property:for i={104,105,106} the fixed points of A008472(i)
%e i.e. values of A075860(i) are uniformly equal to 2.
%t ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] sopf[x_] := Apply[Plus, ba[x]] Do[s=Length[Union[tik=Table[FixedPoint[sopf, j], {j, 1+Prime[n], -1+Prime[n+1]}]]]; If[Equal[s, 1]&&!PrimeQ[2+Prime[n]], Print[Prime[n]]], {n, 1, 100000}]
%Y Cf. A008472, A075860, A082880-A082882.
%K nonn
%O 1,1
%A _Labos Elemer_, Apr 16 2003
|
