cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

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

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Author

Rémy Sigrist, Jan 08 2020

Keywords

Comments

In other words, a(n) is the greatest prime prefix of n, or 0 if every prefix of n is nonprime.
This sequence is a decimal variant of A039634.

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.
		

Crossrefs

See A331045 for a similar sequence.

Programs

  • Mathematica
    A331044[n_] := NestWhile[Quotient[#, 10] &, n, # > 0 && !PrimeQ[#] &];
    Array[A331044, 100, 0] (* Paolo Xausa, Nov 22 2024 *)
  • 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.

A331046 Numbers k such that floor(k/10^m) is a prime number for some m >= 0.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83, 89, 97, 101, 103, 107, 109, 110, 111, 112, 113
Offset: 1

Views

Author

Rémy Sigrist, Jan 08 2020

Keywords

Comments

In other words, these are the numbers with a prime prefix.
For any m > 0:
- let f(m) be the proportion of positive numbers <= 10^m belonging to this sequence,
- we have f(m) = Sum_{p < 10^m in A069090} 1/10^A055642(p),
- also f(m) <= f(m+1) <= 1,
- so {f(m)} has a limit, say F, as m tends to infinity,
- what is the value of F?

Examples

			The number 2 is prime, so every number in A217394 belongs to this sequence.
		

Crossrefs

Cf. A055642, A069090, A202259 (complement), A217394, A331044, A331045.

Programs

  • PARI
    is(n,base=10) = while (n, if (isprime(n), return (1), n\=base)); return (0)
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