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A166504
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Slime numbers: numbers which are the concatenation of primes, with "leading zeros" allowed.
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6
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2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 47, 52, 53, 55, 57, 59, 61, 67, 71, 72, 73, 75, 77, 79, 83, 89, 97, 101, 103, 107, 109, 112, 113, 115, 117, 127, 131, 132, 133, 135, 137, 139, 149, 151, 157, 163, 167, 172, 173, 175, 177, 179
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OFFSET
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1,1
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COMMENTS
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A number is in this sequence if and only if it is prime or of the form a(k)*10^m+a(n), where a(k), a(n) are in this sequence and 10^m >= a(n) (and from this follows that one among a(k), a(n) can be taken to be prime).
This contains A152242 as a subsequence, but also additional terms like e.g. 202 which can be split into two primes, 2 and 02 (= 2). Such a splitting, where some of the substrings contain leading zeros, is not allowed in A152242.
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LINKS
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PROG
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(PARI) is_A166504(n)={ isprime(n) | ((bittest(n, 0) | n%10==2) & for(i=1, #Str(n)-1, isprime(n%10^i) & is_A166504(n\10^i) & return(1)))}
(PARI) is(n)=if(isprime(n), return(1)); if(n<202, return(isprime(n%10)&&isprime(n\10))); my(k=n%10, v); if(k==5||k==2, return(if(n<6, 1, n\=10; has(n/10^valuation(n, 10))))); if(k%2==0, return(0)); v=digits(n); for(i=1, #v, if(isprime(n%10^i)&&is(n\10^i), return(1))); 0 \\ Charles R Greathouse IV, Apr 30 2013
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CROSSREFS
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Cf. A152242 (no leading zeros allowed).
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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