A331044 a(n) is the greatest prime number of the form floor(n/10^k) for some k >= 0, or 0 if no such prime number exists.
0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 2, 2, 2, 23, 2, 2, 2, 2, 2, 29, 3, 31, 3, 3, 3, 3, 3, 37, 3, 3, 0, 41, 0, 43, 0, 0, 0, 47, 0, 0, 5, 5, 5, 53, 5, 5, 5, 5, 5, 59, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 7, 71, 7, 73, 7, 7, 7, 7, 7, 79, 0
Offset: 0
Examples
For n = 42: - neither 42 nor 4 is a prime number, - hence a(42) = 0. For n = 290: - 290 is not a prime number, - 29 is a prime number, - hence a(290) = 29.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
A331044[n_] := NestWhile[Quotient[#, 10] &, n, # > 0 && !PrimeQ[#] &]; Array[A331044, 100, 0] (* Paolo Xausa, Nov 22 2024 *)
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PARI
a(n, base=10) = while (n, if (isprime(n), return (n), n\=base)); 0
Formula
a(n) <= n with equality iff n = 0 or n is a prime number.
a(n) >= 0 with equality iff n belongs to A202259.
Comments