A083684 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.

3, 10, 16, 28, 34, 40, 46, 52, 70, 76, 82, 88, 97, 103, 121, 127, 136, 163, 166, 169, 175, 187, 199, 205, 211, 217, 220, 235, 250, 262, 268

Offset: 1

Author

Farideh Firoozbakht, Jun 15 2003

Keywords

• nonn
• base
• more

Comments

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

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

Examples

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

Crossrefs

Cf. A082549, A083677.

Programs

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

Extensions

Corrected and edited by Farideh Firoozbakht, Nov 04 2013