A082883 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.

103, 457, 1009, 1663, 2953, 3079, 6043, 12007, 17707, 20749, 21499, 25579, 28537, 30703, 41227, 54367, 55663, 59443, 66973, 70309, 81547, 83557, 90019, 97003, 101359, 102559, 105367, 108499, 116239, 120847, 126019, 129733, 133873, 138403

Offset: 1

Author

Labos Elemer, Apr 16 2003

Keywords

• nonn

Examples

			p[2033]=17007 is here because next prime is 17013;
for the five j inter-prime composites
i.e. if j is from {17008,..,17012} the values
of A075860 are identical: {7,7,7,7,7}, so A082882(2033)=1;
Smallest such example is a(1)=103 with this sophisticated
property:for i={104,105,106} the fixed points of A008472(i)
i.e. values of A075860(i) are uniformly equal to 2.
		

Crossrefs

Cf. A008472, A075860, A082880-A082882.

Programs

Mathematica

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}]