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A276481 Numbers k such that b(k) is prime, where b(1) = prime(1) = 2, b(n) = 10*b(n-1) + (prime(n) mod 10).

%I A276481 #25 Aug 12 2025 06:09:36
%S A276481 1,2,4,13,16,17,28,34,90,100,132,331,534,7923,10157,40197
%N A276481 Numbers k such that b(k) is prime, where b(1) = prime(1) = 2, b(n) = 10*b(n-1) + (prime(n) mod 10).
%C A276481 Primes in the sequence b(n) are 2, 23, 2357, 2357137939171, ...
%C A276481 a(17) > 50000. - _Michael S. Branicky_, Aug 12 2025
%F A276481 {k | A386964(k) is prime}. - _Michael S. Branicky_, Aug 12 2025
%p A276481 Res:= NULL: p:= 0: b:= 0:
%p A276481 for n from 1 to 600 do
%p A276481   p:= nextprime(p);
%p A276481   b:= 10*b + (p mod 10);
%p A276481   if isprime(b) then Res:= Res, n fi
%p A276481 od:
%p A276481 Res; # _Robert Israel_, Sep 05 2016
%t A276481 b[1] = Prime@ 1; b[n_] := b[n] = 10 b[n - 1] + Mod[Prime@ n, 10]; Select[Range[10^3], PrimeQ@ b[#] &] (* _Michael De Vlieger_, Sep 06 2016 *)
%o A276481 (PARI) b(n) = if (n==1, 2, 10*b(n-1) + (prime(n) % 10));
%o A276481 isok(n) = isprime(b(n)); \\ _Michel Marcus_, Sep 05 2016
%o A276481 (PARI) list(lim)=my(v=List(),s,n); forprime(p=2,, if(n++>lim, return(Vec(v))); if(ispseudoprime(s=10*s+p%10), listput(v, n))) \\ _Charles R Greathouse IV_, Sep 05 2016
%Y A276481 Cf. A007652, A069151, A386964.
%K A276481 nonn,base
%O A276481 1,2
%A A276481 _Thomas Ordowski_, Sep 05 2016
%E A276481 a(7)-a(13) from _Michel Marcus_, Sep 05 2016
%E A276481 a(14) from _Robert Israel_, Sep 05 2016
%E A276481 a(15)-a(16) from _Michael S. Branicky_, Aug 11 2025