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A083684 Numbers n such that there is no nonnegative integer m such that m < n*prime(n) and the concatenated decimal number fp(n,m) = prime(1).m.prime(2).m. ... .prime(n-1).m.prime(n) 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

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

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

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

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.

Sequence in context: A278041 A063209 A063109 * A141497 A059911 A160375

Adjacent sequences:  A083681 A083682 A083683 * A083685 A083686 A083687

KEYWORD

nonn,base

AUTHOR

Farideh Firoozbakht, Jun 15 2003

EXTENSIONS

Corrected and edited by Farideh Firoozbakht, Nov 04 2013

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)