A039634 -id:A039634 - cp's OEIS frontend

A039640 Fixed point of "k -> k/2 or (k+1)/2 until result is prime", starting with prime(n)-1.

1, 2, 2, 3, 5, 3, 2, 5, 11, 7, 2, 5, 5, 11, 23, 13, 29, 2, 17, 5, 5, 5, 41, 11, 3, 13, 13, 53, 7, 7, 2, 17, 17, 5, 37, 19, 5, 41, 83, 43, 89, 23, 3, 3, 13, 13, 53, 7, 113, 29, 29, 2, 2, 2, 2, 131, 67, 17, 5, 5, 71, 73, 5, 5, 5, 79, 83, 11, 173, 11, 11, 179, 23, 47, 3, 191, 97, 13

Offset: 1

Wouter Meeussen

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A039634-A039645.

Cf. A010051, A000040, A039644, A039638, A039635.

a039640 1 = 1
a039640 n = until ((== 1) . a010051) (flip div 2 . (+ 1)) (a000040 n - 1)
-- Reinhard Zumkeller, Nov 17 2013

Mathematica
```
(* See A039635. *)
```

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039641 Fixed point of "k -> k/2 or (k+1)/2 until result is prime", starting with prime(n)+1.

Original entry on oeis.org

3, 2, 3, 2, 3, 7, 5, 5, 3, 2, 2, 19, 11, 11, 3, 7, 2, 31, 17, 5, 37, 5, 11, 23, 13, 13, 13, 7, 7, 29, 2, 17, 5, 5, 19, 19, 79, 41, 11, 11, 23, 23, 3, 97, 13, 13, 53, 7, 29, 29, 59, 2, 61, 2, 17, 17, 17, 17, 139, 71, 71, 37, 5, 5, 157, 5, 83, 43, 11, 11, 89, 23, 23, 47, 3, 3, 13

Offset: 1

Wouter Meeussen

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A039634-A039645.

Cf. A010051, A000040, A039645, A039639, A039635.

a039641 = until ((== 1) . a010051) (flip div 2 . (+ 1)) . (+ 1) . a000040
-- Reinhard Zumkeller, Nov 17 2013

(* See A039635. *)
Table[NestWhile[If[EvenQ[#],#/2,(#+1)/2]&,n+1,!PrimeQ[#]&],{n,Prime[ Range[ 80]]}] (* Harvey P. Dale, May 12 2014 *)

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039642 Number of steps to fixed point of "k -> k/2 or (k-1)/2 until result is prime", starting with prime(n)-1.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 4, 4, 2, 3, 3, 5, 4, 4, 2, 3, 2, 4, 6, 3, 6, 3, 2, 4, 6, 6, 6, 2, 4, 5, 3, 7, 4, 4, 3, 3, 4, 6, 2, 3, 2, 5, 3, 7, 7, 7, 5, 5, 2, 6, 4, 3, 6, 4, 8, 2, 3, 3, 5, 5, 5, 3, 5, 5, 5, 3, 4, 7, 2, 4, 6, 2, 6, 5, 4, 2, 3, 8, 8, 8, 6, 6, 3, 6, 3, 6, 7, 7, 7, 7, 2, 2, 7, 4, 5, 2, 3, 9, 9, 4, 6, 3

Offset: 1

Wouter Meeussen

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A039634-A039645.

Cf. A010051, A000040, A039638, A039644, A039636.

a039642 1 = 1
a039642 n = snd $ until ((== 1) . a010051 . fst)
                  (\(x, i) -> (x `div` 2 , i + 1)) (a000040 n - 1, 1)
-- Reinhard Zumkeller, Nov 17 2013

Mathematica
```
(* See A039636. *)
```

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039643 Number of steps to fixed point of "k -> k/2 or (k-1)/2 until result is prime", starting with prime(n)+1.

Original entry on oeis.org

1, 2, 2, 3, 3, 2, 4, 3, 4, 3, 5, 2, 4, 3, 5, 3, 4, 2, 3, 6, 2, 5, 5, 4, 6, 6, 4, 4, 4, 5, 7, 7, 4, 4, 3, 4, 2, 3, 6, 3, 5, 5, 7, 2, 7, 7, 3, 6, 6, 6, 4, 6, 6, 4, 8, 8, 3, 5, 2, 5, 3, 3, 5, 5, 2, 3, 3, 7, 4, 4, 6, 6, 5, 5, 4, 8, 3, 2, 8, 8, 6, 2, 6, 6, 6, 6, 7, 2, 7, 5, 5, 7, 4, 4, 5, 5, 3, 9, 3, 2, 3, 3

Offset: 1

Wouter Meeussen

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A039634-A039645.

Cf. A010051, A000040, A039639, A039645, A039636.

a039643 n = snd $ until ((== 1) . a010051 . fst)
                  (\(x, i) -> (x `div` 2 , i + 1)) (a000040 n + 1, 1)
-- Reinhard Zumkeller, Nov 17 2013

Mathematica
```
(* See A039636. *)
```

Offset corrected by Reinhard Zumkeller, Nov 17 2013

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

Rémy Sigrist, Jan 08 2020

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.

			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.

Rémy Sigrist, Table of n, a(n) for n = 0..10000

See A331045 for a similar sequence.

Cf. A039634, A202259, A320584.

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

a(n, base=10) = while (n, if (isprime(n), return (n), n\=base)); 0

a(n) <= n with equality iff n = 0 or n is a prime number.

a(n) >= 0 with equality iff n belongs to A202259.

cp's OEIS Frontend

A039640 Fixed point of "k -> k/2 or (k+1)/2 until result is prime", starting with prime(n)-1.

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A039641 Fixed point of "k -> k/2 or (k+1)/2 until result is prime", starting with prime(n)+1.

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A039642 Number of steps to fixed point of "k -> k/2 or (k-1)/2 until result is prime", starting with prime(n)-1.

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Haskell

Mathematica

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A039643 Number of steps to fixed point of "k -> k/2 or (k-1)/2 until result is prime", starting with prime(n)+1.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

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.

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