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A083684
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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