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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

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.

PROG

(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

CROSSREFS

Cf. A082549, A083677.

Sequence in context: A278041 A063209 A063109 * A141497 A059911 A160375

Adjacent sequences:  A083681 A083682 A083683 * A083685 A083686 A083687

KEYWORD

nonn,base,more

AUTHOR

Farideh Firoozbakht, Jun 15 2003

EXTENSIONS

Corrected and edited by Farideh Firoozbakht, Nov 04 2013

STATUS

approved

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Last modified September 30 03:30 EDT 2020. Contains 337432 sequences. (Running on oeis4.)