2,1

In the standard binomial transform of the primes most of the terms are composite.

Sum of right diagonal (end number of each delta row) of transform + next prime of the above sequence creates the next transform prime.

This is the binomial transform of the new sequence.

2,5,13,37,101,271,727,1931,5003,12547,30449,71761,165037,

372149,826303,1813219,3944921,8533073,18393821,39588071,

85192381,183479291,395667617,854417989,1847225579,3996807053,

8650687127,18721431499,40496966207,87538925959,189076973699,

408090258677,880275573349,1898072186453,4091892797737,

8820984877351,19015949525137,40992990314189,88355012668999,

190364989602967,409882270030033,881700809985239,

1894318010182909,4063965944848079,8704271352438569,..

The prime 7 and various larger primes are missing from the new sequence because the transform would not consist of primes. For example,

2,5,13,33

3,8 20

5,12

7

and 33 is not prime, so we must eliminate 7.

Cf. A007443.

Sequence in context: A032024 A131741 A096650 this_sequence A129201 A137692 A004680

Adjacent sequences: A111104 A111105 A111106 this_sequence A111108 A111109 A111110

easy,nonn

Dan Joyce (30pack(AT)sbcglobal.net), Oct 14 2005