A270264 The cumulative sum of the digits of successive terms reproduces the prime number sequence; this is the lexicographically earliest sequence with this property.

2, 1, 11, 20, 4, 101, 13, 110, 22, 6, 200, 15, 31, 1001, 40, 24, 33, 1010, 42, 103, 1100, 51, 112, 60, 8, 121, 2000, 130, 10001, 202, 59, 211, 105, 10010, 19, 10100, 114, 123, 220, 132, 141, 11000, 28, 20000, 301, 100001, 39, 48, 310, 100010, 400, 150, 100100, 37, 204, 213, 222, 101000, 231, 1003, 110000, 46, 68, 1012, 200000, 1021, 77, 240, 55, 1000001, 1030, 303, 17, 312, 321, 1102, 330, 26, 1111, 35, 64, 1000010, 73, 1000100, 402, 1120, 411, 44

Offset

1,1

Comments

Add the digits of (say) the first 4 terms of the sequence: you'll get 7 and 7 is the 4th prime number.

Add the digits of the first 5 terms of the sequence: you'll get 11 and 11 is the 5th prime number.

Add the digits of the first 6 terms of the sequence: you'll get 13 and 13 is the 6th prime number. Etc.

Presumably this is a permutation of the numbers {1} union A054683 (cf. A269740). - N. J. A. Sloane, Mar 15 2016

The conjecture that the sequence is equal to {1} union A054683 is equivalent to Polignac's conjecture (a generalization of the twin prime conjecture) which is still open. - Chai Wah Wu, Mar 15 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A054683.

A269740 says where n-th term of A054683 appears.

Sequence in context: A063624 A101851 A300455 * A305877 A111724 A184299

Adjacent sequences: A270261 A270262 A270263 * A270265 A270266 A270267

Keyword

nonn,base,nice

Author

Eric Angelini and Jean-Marc Falcoz, Mar 14 2016

Status

approved