A075519 -id:A075519 - cp's OEIS frontend

A075518 a(n) = floor(prime(n)/4).

0, 0, 1, 1, 2, 3, 4, 4, 5, 7, 7, 9, 10, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 25, 26, 27, 28, 31, 32, 34, 34, 37, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 49, 52, 55, 56, 57, 58, 59, 60, 62, 64, 65, 67, 67, 69, 70, 70, 73, 76, 77, 78, 79, 82, 84, 86, 87, 88, 89, 91

Offset: 1

Reinhard Zumkeller, Sep 19 2002

a(n)*4 + A039702(n) = A000040(n).

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

Cf. A075519.

a075518 = (`div` 4) . a000040  -- Reinhard Zumkeller, Oct 10 2013

Floor[Prime[Range[80]]/4] (* Harvey P. Dale, Dec 27 2011 *)

a(n) = prime(n) \ 4; \\ Joerg Arndt, Aug 04 2013

A075522 Number of steps to reach the first nonprime (=A075523(n)) starting with the n-th prime p and iterating the map k -> 4*k+(p mod 4), or -1 if no integer is ever reached.

Original entry on oeis.org

1, 1, 1, 3, 3, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4

Offset: 1

Reinhard Zumkeller, Sep 19 2002

nonn

a(A075521(n)) > 1;

a(n) = a(A075520(n))+1 for n with A075520(n) prime.

			A000040(4)=7 and (7 mod 4) = 3: 7 -> 4*7+3=31 -> 4*31+3=127 -> 4*127+3=511 = A075523(4), therefore a(4)=3.

Cf. A075520, A075519.

A168446 Primes p such that floor(p/5) is also prime.

Original entry on oeis.org

11, 13, 17, 19, 29, 37, 59, 67, 89, 97, 149, 157, 239, 269, 307, 337, 359, 367, 397, 419, 449, 487, 509, 547, 569, 659, 757, 787, 839, 907, 967, 997, 1117, 1259, 1289, 1319, 1409, 1559, 1567, 1657, 1747, 1867, 1949, 1987, 2099, 2287, 2309, 2339, 2399, 2437, 2459

Offset: 1

Vladimir Joseph Stephan Orlovsky, Nov 25 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A075519, A168447.

[p: p in PrimesUpTo(2500) | IsPrime(Floor(p/5))]; // Vincenzo Librandi, Apr 16 2013

Select[Prime[Range[6! ]],PrimeQ[Floor[ #/5]]&]

Definition and values corrected by R. J. Mathar, Dec 06 2009

A168447 Primes p such that floor(p/6) is also prime.

Original entry on oeis.org

13, 17, 19, 23, 31, 43, 47, 67, 71, 79, 83, 103, 107, 139, 179, 191, 223, 227, 251, 263, 283, 359, 367, 431, 439, 443, 479, 499, 503, 587, 607, 619, 643, 647, 659, 683, 787, 823, 827, 839, 907, 911, 947, 983, 1039, 1087, 1091, 1151, 1163, 1187, 1367, 1399

Offset: 1

Vladimir Joseph Stephan Orlovsky, Nov 25 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A075519, A168446.

[p: p in PrimesUpTo(1400) | IsPrime(Floor(p/6))]; // Vincenzo Librandi, Apr 16 2013

Select[Prime[Range[6! ]],PrimeQ[Floor[ #/6]]&]

is(n)=isprime(n) && isprime(n\6) \\ Charles R Greathouse IV, Feb 23 2017

a(n) >> n log^2 n. - Charles R Greathouse IV, Feb 23 2017

Definition corrected by R. J. Mathar, Dec 06 2009

cp's OEIS Frontend

A075518 a(n) = floor(prime(n)/4).

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A075522 Number of steps to reach the first nonprime (=A075523(n)) starting with the n-th prime p and iterating the map k -> 4*k+(p mod 4), or -1 if no integer is ever reached.

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A168446 Primes p such that floor(p/5) is also prime.

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A168447 Primes p such that floor(p/6) is also prime.

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Magma

Mathematica

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