A158754 Courteous prime numbers.

31, 41, 101, 109, 137, 191, 193, 239, 283, 311, 313, 569, 641, 659, 661, 821, 1091, 1153, 1289, 1291, 1301, 1303, 1319, 1429, 1453, 1619, 1667, 1877, 2027, 2081, 2129, 2239, 2309, 2341, 2381, 2591, 2593, 2711, 2713, 2971, 3001, 3121, 3253, 3299, 3301

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 25 2009

Keywords

• nonn

Comments

Courteous prime numbers are twin prime numbers and can be written as the sum of two or more consecutive twin prime numbers. 7+11+13=31,11+13+17=41,..

Crossrefs

Cf. A138591, A065867

Programs

Mathematica

lst={};Do[pp=Prime[m];If[PrimeQ[pp-2]||PrimeQ[pp+2],k=1;Do[k++;p=Prime[n];If[PrimeQ[p-2]||PrimeQ[p+2],pp+=p;If[PrimeQ[pp],If[PrimeQ[pp-2]||PrimeQ[pp+2],AppendTo[lst,pp]]]],{n,m+1,4*6!}]],{m,1,4*6!}];lst;(*Courteous Prime Numbers.*)Take[Union[lst],5! ]
upto=3400;With[{tps=Union[Flatten[Select[Partition[Prime[Range[ PrimePi[ upto]]], 2,1], Last[#]-First[#]==2&]]]}, Select[Union[Flatten[Table[ Total/@Partition[tps,n,1],{n,2,40}]]],MemberQ[tps,#]&&#<=upto&]] (* Harvey P. Dale, Sep 25 2011 *)