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A175523 a(n)=a(n-1)+ p, where p is the least prime whose first digit equals the first digit of a(n-1) and p>=a(n-1).

%I A175523 #10 Jun 02 2025 02:47:54
%S A175523 1,12,25,54,113,226,453,910,1821,3644,7303,14610,29231,58462,116939,
%T A175523 233892,467803,935616,1871237,3742486,7484979,14969998,29939999,
%U A175523 59880012,119760031,239520072,479040191,958080388,1916160779,3832321566
%N A175523 a(n)=a(n-1)+ p, where p is the least prime whose first digit equals the first digit of a(n-1) and p>=a(n-1).
%e A175523 a(0)=1, least prime >=1 with the first digit 1 is 11, so a(1)=1+11=12, least prime >=12 with the first digit 1 is 13, so a(2)=12+13=25, least prime >=25 with the first digit 2 is 29, so a(3)=25+29=54, ...etc.
%p A175523 A000030 := proc(n) op(-1,convert(n,base,10)) ; end proc:
%p A175523 A175523 := proc(n) option remember; if n = 1 then 1; else a1 := procname(n-1) ; fda := A000030(a1) ; p := nextprime(a1-1) ; while true do if A000030(p) = fda then return p+a1 ; end if; p := nextprime(p) ; end do: end if; end proc:
%p A175523 seq(A175523(n),n=1..30); # _R. J. Mathar_, Dec 05 2010
%Y A175523 Cf.A000040
%K A175523 nonn,base,easy,less
%O A175523 1,2
%A A175523 _Ctibor O. Zizka_, Dec 03 2010