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%I #21 Jul 12 2014 17:52:24
%S 2,29,227,22807,86269,2206031,668880743,4208046655963
%N Least primes x that remain primes for n steps under the transform T(x) as defined in A243993.
%C Only primes with most significant digit even.
%e n=0: 2
%e n=1: 29 -> 11
%e n=2: 227 -> 499 -> 383
%e n=3: 22807 -> 40879 -> 48563 -> 23197
%e n=4: 86269 -> 48857 -> 26321 -> 89533 -> 74861
%e n=5: 2206031 -> 4266343 -> 6829777 -> 4016443 -> 4170877 -> 5878541
%e n=6: 668880743 -> 246687179 -> 602458861 -> 626936477 -> 885290143 -> 637191571 -> 908006287
%e n=7: 4208046655963 -> 6288402104597 -> 8062423149463 -> 8686654533091 -> 4442199863909 -> 8863087492993 -> 6493851311821 -> 321364429037.
%p with(numtheory);
%p T:=proc(t) local j,w,x,y; x:=t; y:=[]; while x>0 do
%p y:=[x mod 10,op(y)]; x:=trunc(x/10); od; w:=(y[nops(y)]+y[1]) mod 10;
%p x:=0; for j from 1 to nops(y)-1 do x:=x*10+((y[j]+y[j+1]) mod 10); od; x:=x*10+w; end:
%p P:=proc(q) local a,b,n,v; v:=array(0..50);
%p for n from 0 to 50 do v[n]:=0; od; v[0]:=2; lprint(0,2);
%p for n from 1 by 2 to q do if isprime(n) then b:=-1; a:=n;
%p while isprime(a) do b:=b+1; a:=T(a); od; if v[b]=0 then
%p v[b]:=n; lprint(b,n); fi; fi; od; end: P(10^10);
%Y Cf. A243993.
%K nonn,more
%O 0,1
%A _Paolo P. Lava_, Jul 01 2014
%E a(7) from _Giovanni Resta_, Jul 03 2014
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