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 1-4 of 4 results.

A007811 Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes.

Original entry on oeis.org

1, 10, 19, 82, 148, 187, 208, 325, 346, 565, 943, 1300, 1564, 1573, 1606, 1804, 1891, 1942, 2101, 2227, 2530, 3172, 3484, 4378, 5134, 5533, 6298, 6721, 6949, 7222, 7726, 7969, 8104, 8272, 8881, 9784, 9913, 10111, 10984, 11653, 11929, 12220, 13546, 14416, 15727
Offset: 1

Views

Author

N. J. A. Sloane and J. H. Conway, Mar 15 1996

Keywords

Links

Crossrefs

Cf. A024912, A102338, A102342, A102700, A007530, A014561, A008471, A032352, A216292, A216293, A125855.
Cf. A010051, A245304, A245305.

Programs

  • Haskell
    a007811 n = a007811_list !! (n-1)
a007811_list = map (pred . head) $ filter (all (== 1) . map a010051') $
   iterate (zipWith (+) [10, 10, 10, 10]) [1, 3, 7, 9]
-- Reinhard Zumkeller, Jul 18 2014
  • Magma
    [n: n in [0..10000] | forall{10*n+r: r in [1,3,7,9] | IsPrime(10*n+r)}]; // Bruno Berselli, Sep 04 2012
  • Maple
    for n from 1 to 10000 do m := 10*n: if isprime(m+1) and isprime(m+3) and isprime(m+7) and isprime(m+9) then print(n); fi: od: quit
  • Mathematica
    Select[ Range[ 1, 10000, 3 ], PrimeQ[ 10*#+1 ] && PrimeQ[ 10*#+3 ] && PrimeQ[ 10*#+7 ] && PrimeQ[ 10*#+9 ]& ]
Select[Range[15000], And @@ PrimeQ /@ ({1, 3, 7, 9} + 10#) &] (* Ray Chandler, Jan 12 2007 *)
  • PARI
    p=2;q=3;r=5;forprime(s=7,1e5,if(s-p==8 && r-p==6 && q-p==2 && p%10==1, print1(p", ")); p=q;q=r;r=s) \\ Charles R Greathouse IV, Mar 21 2013
  • Perl
    use ntheory ":all"; my @s = map { ($-1)/10 } sieve_prime_cluster(10,1e9, 2,6,8); say for @s; # _Dana Jacobsen, May 04 2017

Formula

a(n) = 3*A014561(n) + 1. - Zak Seidov, Sep 21 2009

A032352 Numbers k such that there is no prime between 10*k and 10*k+9.

Original entry on oeis.org

20, 32, 51, 53, 62, 84, 89, 107, 113, 114, 126, 133, 134, 135, 141, 146, 150, 164, 167, 168, 171, 176, 179, 185, 189, 192, 196, 204, 207, 210, 218, 219, 232, 236, 240, 248, 249, 251, 256, 258, 282, 294, 298, 305, 309, 314, 315, 317, 323, 324, 326, 328, 342
Offset: 1

Views

Author

Jeff Burch

Keywords

Comments

Numbers k with property that appending any single decimal digit to k does not produce a prime.
A007920(n*10) > 10.

Examples

			m=32: 321=3*107, 323=17*19, 325=5*5*13, 327=3*109, 329=7*47, therefore 32 is a term.

Links

Crossrefs

Cf. A124665 (subsequence), A010051, A007811, A216292, A216293.

Programs

  • Haskell
    a032352 n = a032352_list !! (n-1)
a032352_list = filter
   (\x -> all (== 0) $ map (a010051 . (10*x +)) [1..9]) [1..]
-- Reinhard Zumkeller, Oct 22 2011
  • Magma
    [n: n in [1..350] | IsZero(#PrimesInInterval(10*n, 10*n+9))]; // Bruno Berselli, Sep 04 2012
  • Maple
    a:=proc(n) if map(isprime,{seq(10*n+j,j=1..9)})={false} then n else fi end: seq(a(n),n=1..350); # Emeric Deutsch, Aug 01 2005
  • Mathematica
    f[n_] := PrimePi[10n + 10] - PrimePi[10n]; Select[ Range[342], f[ # ] == 0 &] (* Robert G. Wilson v, Sep 24 2004 *)
Select[Range[342], NextPrime[10 # ] > 10 # + 9 &] (* Maciej Ireneusz Wilczynski, Jul 18 2010 *)
Flatten@Position[10*#+{1,3,7,9}&/@Range@4000,{?CompositeQ ..}] (* _Hans Rudolf Widmer, Jul 06 2024 *)
  • PARI
    is(n)=!isprime(10*n+1) && !isprime(10*n+3) && !isprime(10*n+7) && !isprime(10*n+9) \\ Charles R Greathouse IV, Mar 29 2013
  • Python
    from sympy import isprime
def aupto(limit):
  alst = []
  for d in range(2, limit+1):
    td = [10*d + j for j in [1, 3, 7, 9]]
    if not any(isprime(t) for t in td): alst.append(d)
  return alst
print(aupto(342)) # Michael S. Branicky, May 30 2021

Formula

a(n) ~ n. - Charles R Greathouse IV, Mar 29 2013

Extensions

More terms from Miklos Kristof, Aug 27 2002

A008471 Exactly 3 out of 10m+1, 10m+3, 10m+7, 10m+9 are primes.

Original entry on oeis.org

4, 7, 13, 22, 31, 43, 46, 61, 64, 85, 88, 103, 106, 109, 130, 142, 145, 160, 166, 169, 178, 199, 238, 268, 271, 316, 367, 376, 391, 400, 409, 415, 421, 451, 472, 478, 493, 523, 541, 544, 547, 550, 574
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A007811, A032352, A216292, A216293.

Programs

A216292 Values of k such that there is exactly one prime between 10k and 10k + 9.

Original entry on oeis.org

9, 11, 12, 14, 18, 21, 24, 29, 30, 36, 39, 41, 42, 45, 47, 48, 55, 58, 63, 66, 68, 69, 71, 72, 74, 77, 78, 79, 80, 81, 83, 86, 87, 90, 92, 93, 95, 96, 98, 100, 102, 104, 105, 108, 111, 116, 117, 119, 120, 124, 125, 131, 137, 138, 139, 140, 144, 147, 151, 152
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Examples

			36 is in the sequence because between 360 and 369 there is exactly one prime: 367. [_Bruno Berselli_, Sep 04 2012]

Links

Crossrefs

Cf. A007811, A032352, A078494, A216293.

Programs

  • Magma
    [n: n in [1..200] | IsOne(#PrimesInInterval(10*n, 10*n+9))]; // Bruno Berselli, Sep 04 2012
  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[Length[ps] == 1, AppendTo[t, n]], {n, 0, 199}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[200],PrimePi[10#+9]-PrimePi[10#]==1&] (* Harvey P. Dale, Feb 04 2015 *)
  • PARI
    is(n)=isprime(10*n+1)+isprime(10*n+3)+isprime(10*n+7)+isprime(10*n+9)==1 \\ Charles R Greathouse IV, Sep 07 2012
  • Python
    from itertools import count, islice
from sympy import isprime
def A216292_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda k: sum(int(isprime(10*k+i)) for i in (1,3,7,9)) == 1, count(max(1,startvalue)))
A216292_list = list(islice(A216292_gen(),30)) # Chai Wah Wu, Sep 23 2022

Formula

a(n) ~ 0.1 n log n. - Charles R Greathouse IV, Sep 07 2012
a(n) = floor(A078494(n) / 10). - Charles R Greathouse IV, Sep 07 2012
Showing 1-4 of 4 results.

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

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