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.

Previous Showing 11-14 of 14 results.

A179849 Sum of prime p and next prime after p is divisible by 7.

Original entry on oeis.org

19, 41, 53, 103, 151, 211, 229, 263, 313, 397, 419, 439, 461, 479, 523, 557, 571, 709, 859, 881, 919, 977, 983, 991, 1033, 1049, 1069, 1091, 1103, 1109, 1117, 1171, 1187, 1193, 1279, 1301, 1327, 1427, 1447, 1453, 1489, 1499, 1571, 1621, 1709, 1721, 1747
Offset: 1

Views

Author

Zak Seidov, Jan 10 2011

Keywords

Comments

Also primes p such that the sum of p and next prime after p is a multiple of 14, since for p > 2 the sum of two consecutive primes is even. - Klaus Brockhaus, Jan 11 2011

Examples

			p=19, q=23, p+q=42=7*6=14*3; p=41, q=43, p+q=84=7*12=14*6.

Crossrefs

Cf. A031932 (lower prime of a difference of 14 between consecutive primes), A008596 (multiples of 14).

Programs

  • Magma
    IsA179849:=func< n | IsPrime(n) and (n+NextPrime(n)) mod 14 eq 0 >; [ p: p in PrimesUpTo(2000) | IsA179849(p) ]; // Klaus Brockhaus, Jan 11 2011
  • Mathematica
    fQ[n_] := Block[{q = NextPrime@ n}, Mod[n + q, 7] == 0]; Select[ Prime@ Range@ 300, fQ]
  • PARI
    {q=3;for(n=1,100,p=q;q=nextprime(p+1);(p+q)%7==0&print(p))}

A216290 Values of k such that 100k+1, 100k+3, 100k+7, 100k+9, 100k+13, 100k+27 are consecutive primes.

Original entry on oeis.org

1, 40426, 85405, 191434, 209896, 369853, 598774, 652468, 719986, 797116, 1028749, 1097752, 1874920, 1892458, 1898398, 2041768, 2389861, 2390344, 2462944, 2651881, 3182338, 3230953, 3314239, 3531106, 3717985, 3734347, 3898165, 3940438, 3994096, 4075846, 4523548, 4870279, 5176018
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Examples

			1 is in the sequence as 100*1 + 1 = 101, 100*1 + 3 = 103, 100*1 + 7 = 107, 100*1 + 9 = 109, 100*1 + 13= 113, 100*1 + 27 = 127 are consecutive primes of the form 100k+1, 100k+3, 100k+7, 100k+9, 100k+13, 100k+27 respectively where k = 1. - _David A. Corneth_, Jun 21 2022

Links

Crossrefs

Cf. A022006, A031932.

Programs

  • PARI
    is(n) = {my(v = [100*n+1,100*n+3,100*n+7,100*n+9,100*n+13,100*n+27], t = 0); forprime(p = 100*n+1, oo, t++; if(v[t] != p, return(0)); if(t >= 6, return(1)))} \\ David A. Corneth, Jun 21 2022
  • Python
    from sympy import nextprime
def ok(n):
    t, targets = 100*n, [100*n+d for d in [1, 3, 7, 9, 13, 27]]
    return all((t:=nextprime(t)) == targets[i] for i in range(6))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jun 21 2022

A231609 Table whose n-th row consists of primes p such that p + 2n is the next prime, read by antidiagonals.

Original entry on oeis.org

3, 7, 5, 23, 13, 11, 89, 31, 19, 17, 139, 359, 47, 37, 29, 199, 181, 389, 53, 43, 41, 113, 211, 241, 401, 61, 67, 59, 1831, 293, 467, 283, 449, 73, 79, 71, 523, 1933, 317, 509, 337, 479, 83, 97, 101, 887, 1069, 2113, 773, 619, 409, 491, 131, 103, 107
Offset: 1

Views

Author

T. D. Noe, Nov 26 2013

Keywords

Comments

The plot has an unusual gap near 10^5. Why?

Examples

			The following sequences are read by antidiagonals
{   3,    5,   11,   17,   29,   41,   59,   71,  101,  107, ...}
{   7,   13,   19,   37,   43,   67,   79,   97,  103,  109, ...}
{  23,   31,   47,   53,   61,   73,   83,  131,  151,  157, ...}
{  89,  359,  389,  401,  449,  479,  491,  683,  701,  719, ...}
{ 139,  181,  241,  283,  337,  409,  421,  547,  577,  631, ...}
{ 199,  211,  467,  509,  619,  661,  797,  997, 1201, 1237, ...}
{ 113,  293,  317,  773,  839,  863,  953, 1409, 1583, 1847, ...}
{1831, 1933, 2113, 2221, 2251, 2593, 2803, 3121, 3373, 3391, ...}
{ 523, 1069, 1259, 1381, 1759, 1913, 2161, 2503, 2861, 3803, ...}
{ 887, 1637, 3089, 3413, 3947, 5717, 5903, 5987, 6803, 7649, ...}
...

Links

Crossrefs

Cf. A001359, A029710, A031924, A031926, A031928.
Cf. A031930, A031932, A031934, A031936, A031938.
Cf. A000230 (numbers in first column).

Programs

  • Mathematica
    nn = 10; t = Table[{}, {nn}]; complete = 0; lastP = 3; While[complete < nn, p = NextPrime[lastP]; diff = p - lastP; If[diff <= 2*nn && Length[t[[diff/2]]] < nn - diff/2 + 1, AppendTo[t[[diff/2]], lastP]; If[Length[t[[diff/2]]] == nn - diff/2 + 1, complete++]]; lastP = p]; t2 = PadRight[t, {nn, nn}, 0]; Table[t2[[n-j+1, j]], {n, nn}, {j, n}]

A052259 Last filtering prime (A052180) of primes p such that next prime is p+14.

Original entry on oeis.org

11, 13, 17, 19, 29, 13, 31, 17, 37, 43, 23, 23, 11, 19, 31, 19, 17, 13, 59, 29, 19, 23, 53, 41, 11, 61, 67, 17, 13, 47, 19, 53, 19, 73, 53, 11, 23, 37, 23, 13, 71, 29, 83, 41, 17, 43, 79, 79, 41, 19, 83, 37, 53, 19, 79, 37, 13, 23, 83, 11, 43, 13, 59, 41, 37, 19, 43, 59, 83
Offset: 1

Views

Author

Labos Elemer, Feb 02 2000

Keywords

Crossrefs

Cf. A031932, A052180.
Previous Showing 11-14 of 14 results.

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