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A084559
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Smallest a(n) > n such that concatenation of numbers from n to a(n) is a prime or 0 if no such number exists.
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6
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OFFSET
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2,1
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COMMENTS
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Terms a(1) and a(10) (and many other terms) are currently unknown.
a(11) = 309, a(12) = 13.
More terms: a(14..17) = (17, 19, 43, 39), a(20) = 23, a(23) = 41, a(25) = 49, a(26) = 147, a(28) = 73, a(33..39) = (103, 37, 603, 37, 43, 57, 43), a(42) = 43, a(44) = 51, a(49) = 241, a(50) = 51, a(n) > 1000 for 12 < n < 50 not mentioned here. - M. F. Hasler, Feb 22 2021
a(10) > 10010, a(18) = 3607, a(66) = 1003, a(275) = 1089. If n == 2 (mod 3), then a(n) == 3 or 5 (mod 6). If n == 0 or 1 (mod 3), then a(n) == 1 (mod 6) (see A341716). - Chai Wah Wu, Feb 22 2021
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LINKS
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EXAMPLE
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a(4) = 7 because 4567 is a prime.
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PROG
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(PARI) A084559(n, N=n, T=10^logint(n, 10))=while(T*=10, for(m=n+1, n=T-1, ispseudoprime(N=N*T+m)&&return(m))) \\ M. F. Hasler, Feb 22 2021
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CROSSREFS
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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EXTENSIONS
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Escape clause added to definition by Chai Wah Wu, Feb 22 2021
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STATUS
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approved
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