A285689 -id:A285689 - cp's OEIS frontend

A285690 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of five primes.

2, 569, 601, 673, 853, 1021, 1069, 1117, 1229, 1277, 1439, 1471, 1543, 1663, 1783, 1831, 1879, 1951, 1999, 2111, 2143, 2251, 2371, 2539, 2647, 2719, 2767, 2879, 2927, 2999, 3079, 3187, 3259, 3307, 3469, 3517, 3637, 3709, 3821, 3853, 4021, 4093, 4201

Offset: 1

Zak Seidov, Apr 24 2017

nonn

First differences: 567, 32, 72, 180, 168, 48, 48, 112, 48, 162, 32, 72, 120, 120, 48, 48, 72, 48, 112, 32, ...

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A255609, A285688, A285689.

A[1]:= 2:
for n from 2 to 100 do
  p:= A[n-1];
  do
    p:= nextprime(p);
    if numtheory:-bigomega(p-A[n-1])=5 then A[n]:= p; break fi
od od:
seq(A[i],i=1..100); # Robert Israel, Nov 04 2019

NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 5, p = NextPrime@ p]; p] &, 2, 40] (* Michael De Vlieger, Apr 25 2017 *)

A285691 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of six primes.

Original entry on oeis.org

2, 1217, 1361, 1601, 1697, 1913, 2129, 2273, 2417, 2633, 2729, 2953, 3049, 3209, 3433, 3529, 3593, 3833, 3929, 4073, 4217, 4441, 4657, 4721, 4817, 5153, 5297, 5393, 5717, 5813, 6029, 6173, 6269, 6829, 7069, 7213, 7309, 7549, 7789

Offset: 1

Zak Seidov, Apr 25 2017

nonn

First differences: 1215, 144, 240, 96, 216, 216, 144, 144, 216, 96, 224, 96, 160, 224, 96, 64, 240, 96, 144, 144, ...

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A255609, A285688, A285689, A285690.

A[1]:= 2: p:= 2: n:= 1:
while n < 60 do
    p:= nextprime(p);
    if numtheory:-bigomega(p-A[n]) = 6 then n:= n+1; A[n]:= p;
    fi
od:
seq(A[i],i=1..60); # Robert Israel, Nov 28 2019

NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 6, p = NextPrime@ p]; p] &, 2, 38] (* Michael De Vlieger, Apr 25 2017 *)

A285692 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of 7 primes.

Original entry on oeis.org

2, 9479, 9767, 10247, 10567, 11047, 11239, 11527, 11719, 12007, 12487, 12919, 13367, 13687, 13879, 14071, 14503, 14951, 15271, 15559, 15991, 16183, 16631, 16759, 17047, 17239, 17431, 17623, 17911, 18199, 18679, 19687, 20359, 20551, 20743, 21031, 21319, 21751, 21943

Offset: 1

Zak Seidov, Apr 25 2017

nonn

First differences: 9477, 288, 480, 320, 480, 192, 288, 192, 288, 480, 432, 448, 320, 192, 192, 432, 448, 320, 288, 432,...

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A255609, A285688, A285689, A285690, A285691.

A:= Vector(100): A[1]:= 2:
for n from 2 to 100 do
  p:= A[n-1];
  do
    p:= nextprime(p);
  until numtheory:-bigomega(p-A[n-1]) = 7;
  A[n]:= p;
od:
convert(A,list); # Robert Israel, Dec 28 2022

NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 7, p = NextPrime@ p]; p] &, 2, 38] (* Michael De Vlieger, Apr 25 2017 *)

A285693 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of 8 primes.

Original entry on oeis.org

2, 6563, 6947, 7331, 7907, 8291, 8867, 10163, 10739, 11699, 12659, 13043, 13619, 15731, 16691, 17987, 18371, 18947, 19843, 20483, 21059, 23003, 23899, 24763, 25147, 26107, 26683, 27067, 28027, 28283, 28859, 29243, 29819

Offset: 1

Zak Seidov, Apr 25 2017

nonn

First differences: 6561, 384, 384, 576, 384, 576, 1296, 576, 960, 960, 384, 576, 2112,...

Cf. A255609, A285688, A285689, A285690, A285691, A285692.

NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 8, p = NextPrime@ p]; p] &, 2, 32] (* Michael De Vlieger, Apr 25 2017 *)

A285694 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of 10 primes.

Original entry on oeis.org

2, 59051, 62507, 64811, 66347, 67883, 71339, 73643, 81707, 83243, 87083, 89387, 91691, 95531, 99371, 100907, 104491, 110251, 115883, 119723, 121259, 126443, 127979, 136043, 139627, 141931, 143467, 145771, 148331

Offset: 1

Zak Seidov, Apr 25 2017

nonn

First differences: 59049, 3456, 2304, 1536, 1536, 3456, 2304, 8064, 1536, 3840, 2304, 2304, ...

Cf. A255609, A285688, A285689, A285690, A285691, A285692, A285693.

NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 10, p = NextPrime@ p]; p] &, 2, 28] (* Michael De Vlieger, Apr 25 2017 *)

cp's OEIS Frontend

A285690 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of five primes.

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A285691 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of six primes.

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A285692 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of 7 primes.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A285693 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of 8 primes.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A285694 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of 10 primes.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica