A083684 - OEIS

%I #24 Apr 10 2020 08:14:01

%S 3,10,16,28,34,40,46,52,70,76,82,88,97,103,121,127,136,163,166,169,

%T 175,187,199,205,211,217,220,235,250,262,268

%N Numbers k such that there is no nonnegative integer m such that m < k*prime(k) and the concatenated decimal number fp(k,m) = prime(1).m.prime(2).m. ... .prime(k-1).m.prime(k) is prime.

%C If k == 1 (mod 3) and 3 divides 2 + 3 + 5 + ... + prime(k) then k

%C is in the sequence. I conjecture that 3 is the only term of the sequence which is not of this form.

%e For each m, fp(1,m)=2 is prime so 1 is not in the sequence.

%e fp(2,2) = 2.2.3 = 223 is prime and 2 < 2*prime(2) so 2 isn't in the sequence. Also for each m, 5 divides fp(3,m) = 2.m.3.m.5 so fp(3,m) is composite and we deduce that 3 is in the sequence.

%o (PARI) is(k) = for(m=0, k*prime(k), if(ispseudoprime(eval(concat(concat([""], vector(2*k-1, i, if(i%2, prime(1+i\2), m)))))), return(0))); 1; \\ _Jinyuan Wang_, Apr 10 2020

%Y Cf. A082549, A083677.

%K nonn,base,more

%O 1,1

%A _Farideh Firoozbakht_, Jun 15 2003

%E Corrected and edited by _Farideh Firoozbakht_, Nov 04 2013