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A335301
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a(n) = prime(n+1) mod (10^k) where k is the least positive integer such that floor(prime(n)/(10^k)) = floor(prime(n+1)/(10^k)) and prime(n) denotes the n-th prime number.
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2
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3, 5, 7, 11, 3, 7, 9, 23, 9, 31, 7, 41, 3, 7, 53, 9, 61, 7, 71, 3, 9, 83, 9, 97, 101, 3, 7, 9, 13, 27, 31, 7, 9, 49, 51, 7, 63, 7, 73, 9, 81, 91, 3, 7, 9, 211, 23, 7, 9, 33, 9, 41, 51, 7, 63, 9, 71, 7, 81, 3, 93, 307, 11, 3, 7, 31, 7, 47, 9, 53, 9, 67, 73, 9
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OFFSET
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1,1
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COMMENTS
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In other words, a(n) is the smallest suffix to be overlaid on the decimal representation of the n-th prime number to obtain the next prime number.
This sequence has similarities with A274206; here we consider consecutive prime numbers, there consecutive nonnegative integers.
There are no two consecutive equal terms.
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LINKS
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FORMULA
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a(n) <= prime(n+1) with equality iff prime(n+1) is the least prime number with its number of digits and leading digit.
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EXAMPLE
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For n = 42:
- prime(42) = 181 and prime(43) = 191,
- floor(181/(10^1)) = 18 <> 19 = floor(191/(10^1)),
- floor(181/(10^2)) = 1 = floor(191/(10^2)),
- so a(42) = 191 mod (10^2) = 91.
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PROG
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(PARI) { base=10; p=2; forprime (q=p+1, 379, for (k=0, oo, m=base^k; if (q\m == p\m, print1 (q%m", "); p=q; break))) }
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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