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

Author

Eric Angelini and Jean-Marc Falcoz, Mar 14 2016

Keywords

• nonn
• base
• nice

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.