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.

Showing 1-8 of 8 results.

A285688 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of three primes.

Original entry on oeis.org

2, 29, 37, 67, 79, 97, 109, 127, 139, 151, 163, 181, 193, 211, 223, 241, 269, 277, 307, 337, 349, 367, 379, 397, 409, 421, 433, 461, 479, 487, 499, 541, 569, 577, 607, 619, 631, 643, 661, 673, 691, 709, 727, 739, 751, 769, 787, 829, 857, 877, 907, 919, 937, 967, 997, 1009, 1021, 1033
Offset: 1

Views

Author

Zak Seidov, Apr 24 2017

Keywords

Comments

First differences: 27,8,30,12,18,12,18,12,12,12,18,12,18,12,18,28,8,30,30,12,18,12

Crossrefs

Cf. A255609.

Programs

  • Mathematica
    NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 3, p = NextPrime@ p]; p] &, 2, 57] (* Michael De Vlieger, Apr 25 2017 *)

A285689 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of four primes.

Original entry on oeis.org

2, 83, 107, 131, 167, 191, 227, 251, 307, 331, 347, 383, 419, 443, 467, 491, 547, 563, 587, 641, 677, 701, 757, 773, 797, 821, 857, 881, 937, 953, 977, 1013, 1049, 1103, 1163, 1187, 1223, 1259, 1283, 1307, 1361, 1451, 1487, 1511, 1567, 1583, 1607, 1663, 1699, 1723, 1747, 1783, 1823
Offset: 1

Views

Author

Zak Seidov, Apr 24 2017

Keywords

Comments

First differences: 81, 24, 24, 36, 24, 36, 24, 56, 24, 16, 36, 36, 24, 24, 24, 56, 16, 24, 54, 36, 24,...

Links

Crossrefs

Cf. A255609, A285688.

Programs

  • Maple
    A[1]:= 2: p:= 2: n:= 1:
while n < 60 do
    p:= nextprime(p);
    if numtheory:-bigomega(p-A[n]) = 4 then n:= n+1; A[n]:= p; fi
od:
seq(A[i],i=1..60); # Robert Israel, Nov 28 2019
  • Mathematica
    NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 4, p = NextPrime@ p]; p] &, 2, 52] (* Michael De Vlieger, Apr 25 2017 *)

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

Original entry on oeis.org

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

Views

Author

Zak Seidov, Apr 24 2017

Keywords

Comments

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

Links

Crossrefs

Cf. A255609, A285688, A285689.

Programs

  • Maple
    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
  • Mathematica
    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

Views

Author

Zak Seidov, Apr 25 2017

Keywords

Comments

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

Links

Crossrefs

Cf. A255609, A285688, A285689, A285690.

Programs

  • Maple
    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
  • Mathematica
    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

Views

Author

Zak Seidov, Apr 25 2017

Keywords

Comments

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

Links

Crossrefs

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

Programs

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

A289750 a(1) = 3 and a(n+1) - a(n) = 2*p where p is the least possible prime.

Original entry on oeis.org

3, 7, 11, 17, 23, 29, 43, 47, 53, 59, 73, 79, 83, 89, 103, 107, 113, 127, 131, 137, 151, 157, 163, 167, 173, 179, 193, 197, 211, 233, 239, 277, 281, 307, 311, 317, 331, 337, 347, 353, 359, 373, 379, 383, 389, 463, 467, 541, 547, 557, 563, 569, 607, 613, 617, 631, 641, 647, 653, 659
Offset: 1

Views

Author

Zak Seidov, Jul 11 2017

Keywords

Comments

Values of p: 2, 2, 3, 3, 3, 7, 2, 3, 3, 7, 3, 2, 3, 7, 2, 3, 7, 2, 3, 7, 3, 3, 2, 3, 3, 7, 2, 7, 11, 3, 19, 2, 13, 2, 3, 7, 3, 5, 3, 3, 7, 3, 2, 3, 37, 2, 37, 3, 5.
For n > 2, a(n) = A255609(n-1). - Jon E. Schoenfield, Nov 26 2017

Examples

			a(1000) = 23833 = A000040(2651), a(999) = 23819 = A000040(2649), and a(1000)-a(999) = 14 = 2*A000040(4), while 23819 + {4,6,10} are composite.

Links

Crossrefs

Cf. A001223, A255609, A289750.

Programs

  • PARI
    step(n)=forprime(p=2,, if(isprime(n+2*p), return(n+2*p)))
first(n)=my(v=vector(n)); v[1]=3; for(n=2,n, v[n]=step(v[n-1])); v \\ Charles R Greathouse IV, Jul 14 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

Views

Author

Zak Seidov, Apr 25 2017

Keywords

Comments

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

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Zak Seidov, Apr 25 2017

Keywords

Comments

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

Crossrefs

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

Programs

  • Mathematica
    NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 10, p = NextPrime@ p]; p] &, 2, 28] (* Michael De Vlieger, Apr 25 2017 *)
Showing 1-8 of 8 results.

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