%I #29 Sep 11 2023 12:26:50

%S 1,2,3,4,7,13,16,19,21,22,25,28,30,31,34,37,43,46,49,51,52,55,58,60,

%T 61,64,67,73,76,79,85,88,94,97,100,101,102,103,106,109,111,112,115,

%U 118,120,121,124,127,133,136,139,141,142,145,148,150,151,154,157

%N a(n) is the least number greater than a(n-1) such that the sum of the decimal digits of a(n-1) and a(n) is prime.

%C Resulting primes: 3, 5, 7, 11, 11, 11, 17, 13, 7, 11, 17, 13, 7, 11, 17, 17, 17, 23, 19, 13, 17, 23, 19, 13, 17, 23, 23, 23, 29, 29, 29, 29, 29.

%e a(1)=1, a(2)=2, 1+2=3 prime,

%e a(5)=7, a(6)=13, 7+1+3=11 prime,

%e a(6)=13, a(7)=16, 1+3+1+6=11 prime.

%t t = {1}; Do[nxt = t[[-1]] + 1; While[! PrimeQ[Total[IntegerDigits[t[[-1]]]] + Total[IntegerDigits[nxt]]], nxt++]; AppendTo[t, nxt], {100}]; t (* _T. D. Noe_, Nov 14 2011 *)

%t nxt[b_]:=Module[{c=b+1},While[!PrimeQ[Total[IntegerDigits[b]]+Total[IntegerDigits[c]]],c++];c]; NestList[nxt,1,60] (* _Harvey P. Dale_, Sep 11 2023 *)

%K nonn,base

%O 1,2

%A _Zak Seidov_, Nov 13 2011

%E Typo in example corrected by _Vincenzo Librandi_, Nov 13 2011