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 1-3 of 3 results.

A336059 Numbers p such that p, 2p-1, 3p-2, 4p-3 are primes.

Original entry on oeis.org

331, 1531, 3061, 4261, 4951, 6841, 10831, 15391, 18121, 23011, 25411, 26041, 31771, 33301, 40111, 41491, 45061, 49831, 53881, 59341, 65851, 70141, 73771, 78541, 88741, 95461, 96931, 109471, 111721, 112621, 117721, 131311, 133201, 134731, 135301, 150151, 165901
Offset: 1

Views

Author

Jeppe Stig Nielsen, Jul 07 2020

Keywords

Comments

The subset p, 2p-1, 4p-3 is a Cunningham chain of the 2nd kind, cf. A057326.

Links

Crossrefs

Cf. A005382, A057326, A067257, A237189, A336060.

Programs

  • Mathematica
    Select[Range[10^5], AllTrue[{#, 2# - 1, 3# - 2, 4# - 3}, PrimeQ] &] (* Amiram Eldar, Jul 07 2020 *)

Formula

a(n) = A237189(n) + 1.

A237190 Numbers k such that k+1, 2k+1, 3k+1, 4k+1, 5k+1 are five primes.

Original entry on oeis.org

10830, 25410, 26040, 88740, 165900, 196560, 211050, 224400, 230280, 247710, 268500, 268920, 375480, 377490, 420330, 451410, 494340, 512820, 592620, 604170, 735750, 751290, 765780, 799170, 808080, 952680, 975660, 1053690, 1064190, 1132860, 1156170, 1532370, 1559580
Offset: 1

Views

Author

Alex Ratushnyak, Feb 04 2014

Keywords

Comments

A subsequence of A237189.
All terms are divisible by 30, and b(n) = a(n)/30 begins: 361, 847, 868, 2958, 5530, 6552, 7035, 7480, 7676, 8257, 8950, 8964, 12516, 12583, 14011, ...

Links

Crossrefs

Cf. A088250, A064238, A124410, A237189.

Programs

  • Mathematica
    Select[30*Range[52000],AllTrue[#*Range[5]+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 31 2017 *)
  • Python
    from sympy import isprime
for n in range(2000000):
    if isprime(n+1) and isprime(2*n+1) and isprime(3*n+1) and isprime(4*n+1) and isprime(5*n+1):
        print(n, end=', ')

A256230 Numbers n such that neither n nor 2*n is representable as x*y+x+y, where x>=y>1.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 9, 18, 21, 30, 33, 36, 78, 81, 96, 105, 138, 141, 156, 165, 198, 210, 228, 261, 270, 273, 306, 330, 336, 345, 366, 378, 393, 438, 453, 498, 525, 546, 561, 576, 585, 600, 606, 618, 660, 690, 726, 765, 810, 828, 861, 876, 933, 936, 966, 996, 1005, 1008
Offset: 1

Views

Author

Alex Ratushnyak, Mar 19 2015

Keywords

Crossrefs

Cf. A254636, A255362.
Cf. A064238 (also 3*n cannot be represented as x*y+x+y, x>=y>1).
Cf. A237189 (also 3*n and 4*n cannot be represented as x*y+x+y, x>=y>1).

Programs

  • Python
    TOP = 2200
a = [0]*TOP
for y in range(2, TOP//2):
  for x in range(y, TOP//2):
    k = x*y + x + y
    if k>=TOP: break
    a[k]=1
print([n for n in range(TOP//2) if a[n]==0 and a[2*n]==0])
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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