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

1,1

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,..

Links

Table of n, a(n) for n=1..45.

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 *)

Crossrefs

Cf. A138591, A065867

Sequence in context: A284531 A040987 A040180 * A140458 A089318 A364149

Adjacent sequences: A158751 A158752 A158753 * A158755 A158756 A158757

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 25 2009

Status

approved