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A270264 The cumulative sum of the digits of successive terms reproduces the prime number sequence; this is the lexicographically earliest sequence with this property. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 29 03:18 EST 2020. Contains 332353 sequences. (Running on oeis4.)