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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

%I

%S 2,1,11,20,4,101,13,110,22,6,200,15,31,1001,40,24,33,1010,42,103,1100,

%T 51,112,60,8,121,2000,130,10001,202,59,211,105,10010,19,10100,114,123,

%U 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

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

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

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

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

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

%C 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

%H Chai Wah Wu, <a href="/A270264/b270264.txt">Table of n, a(n) for n = 1..10000</a>

%Y Cf. A000040, A054683.

%Y A269740 says where n-th term of A054683 appears.

%K nonn,base,nice

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 14 2016

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Last modified April 9 17:32 EDT 2020. Contains 333361 sequences. (Running on oeis4.)