A111107 - OEIS

A111107

Lexicographically smallest sequence of distinct primes whose binomial transform consists only of primes.

2, 3, 5, 11, 13, 29, 43, 53, 59, 71, 79, 83, 103, 113, 139, 173, 181, 227, 269, 277, 317, 383, 463, 509, 673, 701, 751, 863, 967, 977, 1187, 1201, 1493, 1531, 1609, 1637, 1801, 2153, 2221, 2239, 2371, 2377, 2543, 2557, 2683

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OFFSET

1,1

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

This is the binomial transform of the 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

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

CROSSREFS

Cf. A007443.

Sequence in context: A131741 A277098 A096650 * A186641 A215354 A129201

Adjacent sequences: A111104 A111105 A111106 * A111108 A111109 A111110

KEYWORD

easy,nonn

AUTHOR

Daniel Joyce, Oct 14 2005

STATUS

approved