A039645 -id:A039645 - cp's OEIS frontend

A039634 Fixed point of "n -> n/2 or (n-1)/2 until result is prime".

1, 2, 3, 2, 5, 3, 7, 2, 2, 5, 11, 3, 13, 7, 7, 2, 17, 2, 19, 5, 5, 11, 23, 3, 3, 13, 13, 7, 29, 7, 31, 2, 2, 17, 17, 2, 37, 19, 19, 5, 41, 5, 43, 11, 11, 23, 47, 3, 3, 3, 3, 13, 53, 13, 13, 7, 7, 29, 59, 7, 61, 31, 31, 2, 2, 2, 67, 17, 17, 17, 71, 2, 73, 37, 37, 19, 19, 19, 79, 5, 5

Offset: 1

Wouter Meeussen

a(n) is the largest prime whose binary expansion is an initial substring of n's binary expansion. - Charlie Neder, Oct 27 2018

a(1) = 1 by convention. - David A. Corneth, Oct 27 2018

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

Cf. A039635-A039645, A010051, A039636, A039638, A039639.

a039634 1 = 1
a039634 n = until ((== 1) . a010051) (flip div 2) n
-- Reinhard Zumkeller, Nov 17 2013

ner[ n_Integer ] := FixedPoint[ If[ EvenQ[ # ]&&#>2, #/2, If[ PrimeQ[ # ]||(#=== 1), #, (#-1)/2 ] ]&, n, 20 ]

a(n)=while(n>3 && !isprime(n), n\=2); n \\ Charles R Greathouse IV, Jun 23 2017

from sympy import isprime
def a(n):
    while n>1 and not isprime(n): n>>=1
    return n
print([a(n) for n in range(1, 82)]) # Michael S. Branicky, Jul 24 2023

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039636 Number of steps to fixed point of "n -> n/2 or (n-1)/2 until result is prime".

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 3, 3, 2, 1, 3, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 4, 4, 2, 2, 3, 1, 3, 1, 5, 5, 2, 2, 5, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 5, 5, 5, 5, 3, 1, 3, 3, 4, 4, 2, 1, 4, 1, 2, 2, 6, 6, 6, 1, 3, 3, 3, 1, 6, 1, 2, 2, 3, 3, 3, 1, 5, 5, 2, 1, 5, 5, 2, 2, 4, 1, 4, 4, 3, 3, 2, 2, 6, 1, 6, 6, 6, 1, 6

Offset: 1

Wouter Meeussen

nonn

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

Cf. A039634-A039645.

Cf. A010051, A039634, A039637, A039642, A039643.

a039636 1 = 1
a039636 n = snd $ until ((== 1) . a010051 . fst)
                        (\(x, i) -> (x `div` 2 , i + 1)) (n, 1)
-- Reinhard Zumkeller, Nov 17 2013

nerlist[ n_Integer ] := Length/@Drop[ FixedPointList[ If[ EvenQ[ # ]&&#>2, #/ 2, If[ PrimeQ[ # ]||(#===1), #, (#-1)/2 ] ]&, n, 20 ], -1 ]

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039635 Fixed point of "n -> n/2 or (n+1)/2 until result is prime".

Original entry on oeis.org

1, 2, 3, 2, 5, 3, 7, 2, 5, 5, 11, 3, 13, 7, 2, 2, 17, 5, 19, 5, 11, 11, 23, 3, 13, 13, 7, 7, 29, 2, 31, 2, 17, 17, 5, 5, 37, 19, 5, 5, 41, 11, 43, 11, 23, 23, 47, 3, 13, 13, 13, 13, 53, 7, 7, 7, 29, 29, 59, 2, 61, 31, 2, 2, 17, 17, 67, 17, 5, 5, 71, 5, 73, 37, 19, 19, 5, 5, 79, 5, 41

Offset: 1

Wouter Meeussen

nonn

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

Cf. A039634-A039645.

Cf. A010051, A039637, A039634, A039640, A039641.

a039635 1 = 1
a039635 n = until ((== 1) . a010051) ((flip div 2) . (+ 1)) n
-- Reinhard Zumkeller, Nov 17 2013

upp[ n_Integer ] := FixedPoint[ If[ EvenQ[ # ]&&#>2, #/2, If[ PrimeQ[ # ]||(#=== 1), #, (#+1)/2 ] ]&, n, 20 ]

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039637 Number of steps to fixed point of "n -> n/2 or (n+1)/2 until result is prime".

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 4, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 5, 1, 5, 2, 2, 4, 4, 1, 2, 4, 4, 1, 3, 1, 3, 2, 2, 1, 5, 3, 3, 3, 3, 1, 4, 4, 4, 2, 2, 1, 6, 1, 2, 6, 6, 3, 3, 1, 3, 5, 5, 1, 5, 1, 2, 3, 3, 5, 5, 1, 5, 2, 2, 1, 4, 2, 2, 4, 4, 1, 3, 3, 3, 2, 2, 6, 6, 1, 4, 4, 4, 1, 4

Offset: 1

Wouter Meeussen

nonn

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

Cf. A039634-A039645.

Cf. A010051, A039635, A039636, A039644, A039645.

a039637 1 = 1
a039637 n = snd $ until ((== 1) . a010051 . fst)
                        (\(x, i) -> ((x + 1) `div` 2 , i + 1)) (n, 1)
-- Reinhard Zumkeller, Nov 17 2013

upplist[ n_Integer ] := Length/@Drop[ FixedPointList[ If[ EvenQ[ # ]&&#>2, #/ 2, If[ PrimeQ[ # ]||(#===1), #, (#+1)/2 ] ]&, n, 20 ], -1 ]

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039644 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, 3, 2, 3, 5, 4, 4, 3, 2, 3, 2, 6, 3, 5, 5, 5, 2, 4, 6, 4, 4, 2, 5, 5, 7, 4, 4, 6, 3, 4, 6, 3, 2, 3, 2, 4, 7, 7, 5, 5, 3, 6, 2, 4, 4, 8, 8, 8, 8, 2, 3, 5, 7, 7, 3, 3, 7, 7, 7, 3, 3, 6, 2, 6, 6, 2, 5, 4, 8, 2, 3, 6, 6, 6, 4, 4, 7, 7, 7, 7, 7, 5, 5, 5, 2, 2, 4, 5, 9, 2, 3, 6, 3, 6, 3, 3

Offset: 1

Wouter Meeussen

nonn

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

Cf. A039634-A039645.

Cf. A010051, A000040, A039640, A039642, A039637.

a039644 1 = 1
a039644 n = snd $ until ((== 1) . a010051 . fst)
            (\(x, i) -> ((x + 1) `div` 2 , i + 1)) (a000040 n - 1, 1)
-- Reinhard Zumkeller, Nov 17 2013

Mathematica
```
(* See A039637. *)
```

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039638 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, 5, 3, 2, 2, 11, 7, 7, 2, 5, 5, 23, 13, 29, 7, 2, 17, 2, 19, 41, 11, 3, 3, 3, 53, 13, 7, 31, 2, 17, 17, 37, 37, 19, 5, 83, 43, 89, 11, 47, 3, 3, 3, 13, 13, 113, 7, 29, 59, 7, 31, 2, 131, 67, 67, 17, 17, 17, 73, 19, 19, 19, 79, 41, 5, 173, 43, 11, 179, 11, 23, 47, 191

Offset: 1

Wouter Meeussen

nonn

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

Cf. A039634-A039645.

Cf. A010051, A000040, A039642, A039640, A039634.

a039638 1 = 1
a039638 n = until ((== 1) . a010051) (flip div 2) (a000040 n - 1)
-- Reinhard Zumkeller, Nov 17 2013

(* See A039634. *)
Table[NestWhile[If[EvenQ[#],#/2,(#-1)/2]&,Prime[n]-1,CompositeQ],{n,80}] (* Harvey P. Dale, May 27 2023 *)

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039639 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, 2, 5, 3, 7, 2, 19, 5, 11, 3, 13, 7, 31, 17, 2, 37, 5, 5, 11, 3, 3, 13, 13, 13, 7, 2, 2, 17, 17, 37, 19, 79, 41, 5, 43, 11, 11, 3, 97, 3, 3, 53, 7, 7, 7, 29, 7, 7, 31, 2, 2, 67, 17, 139, 17, 71, 73, 19, 19, 157, 79, 83, 5, 43, 43, 11, 11, 23, 23, 47, 3, 97, 199, 3

Offset: 1

Wouter Meeussen

nonn

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

Cf. A039634-A039645.

Cf. A010051, A000040, A039643, A039641, A039634.

a039639 = until ((== 1) . a010051) (flip div 2) . (+ 1) . a000040
-- Reinhard Zumkeller, Nov 17 2013

Mathematica
```
(* See A039634. *)
```

Offset corrected by Reinhard Zumkeller, Nov 17 2013

A039640 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, 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

cp's OEIS Frontend

A039634 Fixed point of "n -> n/2 or (n-1)/2 until result is prime".

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A039636 Number of steps to fixed point of "n -> n/2 or (n-1)/2 until result is prime".

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A039635 Fixed point of "n -> n/2 or (n+1)/2 until result is prime".

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A039637 Number of steps to fixed point of "n -> n/2 or (n+1)/2 until result is prime".

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A039644 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

A039638 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

A039639 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

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

Views

Author

Keywords

Links

Crossrefs