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 1-5 of 5 results.

A051003 Beastly (or hateful) numbers: numbers containing the string 666 in their decimal expansion.

Original entry on oeis.org

666, 1666, 2666, 3666, 4666, 5666, 6660, 6661, 6662, 6663, 6664, 6665, 6666, 6667, 6668, 6669, 7666, 8666, 9666, 10666, 11666, 12666, 13666, 14666, 15666, 16660, 16661, 16662, 16663, 16664, 16665, 16666, 16667, 16668, 16669, 17666, 18666
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Links

Crossrefs

Cf. A131645, A057564, A002282, A138563, A043515, A046720, A186086.

Programs

  • Mathematica
    Select[Range[18666], ! StringFreeQ[ToString[#], "666"] &] (* Arkadiusz Wesolowski, Sep 08 2011 *)

A131645 Beastly primes (version 2): primes containing 666 as a substring.

Original entry on oeis.org

6661, 16661, 26669, 46663, 56663, 66601, 66617, 66629, 66643, 66653, 66683, 66697, 76667, 96661, 96667, 106661, 106663, 106669, 116663, 146669, 166601, 166603, 166609, 166613, 166619, 166627, 166631, 166643, 166657, 166667, 166669, 166679
Offset: 1

Views

Author

Tanya Khovanova, Sep 08 2007

Keywords

Comments

These are the primes among the beastly numbers A051003.
There are several other definitions of beastly primes (see cross-references).
Asymptotic density n/log(n), since almost all primes are of this form.

Links

Crossrefs

Cf. A051003, A186086, A046720, A138563, A232448, A321001.

Programs

  • Mathematica
    Select[Range[300000], StringFreeQ[ToString[ # ], "666"] == False && PrimeQ[ # ] &]
Select[Prime[Range[300000]],!StringFreeQ[ToString[ # ],"666"]&] (* Zak Seidov, Jan 09 2009 *)
  • PARI
    digitsIn(x) = 1 + log(x)\log(10)
allocatemem(932245000);
default(primelimit, 4294965247); m=1; forprime (p=6660, 68466670, d=digitsIn(p); for (i=1, d-3, t=10^i; u=p\t; x=u-(u\1000)*1000; if (x==666, print(m, " ", p); write("b131645.txt", m, " ", p); m++; break))) \\ Harry J. Smith, Jan 11 2009

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Oct 13 2015

Extensions

Definition corrected by Arkadiusz Wesolowski, Feb 12 2011
Edited by N. J. A. Sloane, Feb 12 2011

A186086 Beastly primes (version 1): either 666 followed by 0's and a 1 or 7 at the right end or a palindrome with 666 in the center, 0's surrounding these digits, and 1 or 7 at both ends.

Original entry on oeis.org

6661, 16661, 66601, 76667, 700666007, 6660000000001, 666000000000001, 700000666000007, 70000006660000007, 6660000000000000000000000007, 66600000000000000000000000007, 1000000000000066600000000000001
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 12 2011

Keywords

Comments

Differs from A131645 in that 26669, 46663, 56663, 66617, 66629, 66643, 66653, 66683, 66697, 96661, 96667, 106661, 106663, 106669, 116663, 146669, 166601, 166603, 166609, 166613, 166619, 166627, 166631, 166643, 166657, 166667, 166669, 166679, are not included here.
76667 is the largest beastly prime that does not contain the digit "0".

Links

Crossrefs

Cf. A046720, A051003, A131645, A164968, A196023, A138563, A186630, A186538, A156166, A186521.

Programs

  • Mathematica
    e = 14; p = 666*10^n + 1; q = (10^(n + 2) + 666)*10^n + 1; Select[Union[Table[p, {n, 2*e}], Table[p + 6, {n, 2*e}], Table[q, {n, e}], Table[q + 6*10^(2*n + 2) + 6, {n, e}]], PrimeQ] (* Arkadiusz Wesolowski, Sep 21 2011 *)
Module[{nn=35,bp1,bp2,bp3,bp4}, bp1=FromDigits/@ Table[Join[PadRight[ {6,6,6},n1,0],{1}],{n1,3,nn}]; bp2=FromDigits/@ Table[Join[ PadRight[ {6,6,6},n2,0],{7}], {n2,3,nn}]; bp3=FromDigits/@ Table[Join[PadRight[ {1},n3,0], {6,6,6},PadLeft[ {1},n3,0]],{n3,1,nn/2}];bp4=FromDigits/@ Table[Join[PadRight[{7},n3,0],{6,6,6}, PadLeft[ {7},n3,0]],{n3,1,nn/2}]; Select[Sort[Join[bp1,bp2,bp3,bp4]],PrimeQ]] (* Harvey P. Dale, Jan 18 2017 *)

Extensions

Edited by N. J. A. Sloane, Feb 12 2011
a(10)-a(12) from Charles R Greathouse IV, Feb 12 2011

A186521 Numbers n>0 such that (7*10^(n+2)+666)*10^n+7 is prime.

Original entry on oeis.org

1, 3, 6, 7, 49, 578, 793, 1322, 1392, 2392, 3066, 13479
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 23 2011

Keywords

Comments

Or, indices of primes in A046720. Rudolf Ondrejka calls these "beastly palindromic primes".
Some of the larger entries may only correspond to probable primes.

Links

Crossrefs

Cf. A046720, A186086.

Programs

  • Mathematica
    Select[Range[10^3], PrimeQ[(7*10^(# + 2) + 666)*10^# + 7] &] (* Arkadiusz Wesolowski, Sep 08 2011 *)

Extensions

a(12) added by Arkadiusz Wesolowski, Mar 16 2011

A260312 Palindromic beastly primes that begin and end with digit '1'.

Original entry on oeis.org

16661, 1000000000000066600000000000001, 10000000000000000000000000000000000000000006660000000000000000000000000000000000000000001
Offset: 1

Views

Author

K. D. Bajpai, Jul 22 2015

Keywords

Comments

The next term a(4) contains 1017 digits, and is too large to include in data section.

Examples

			a(1) = 16661 is a palindromic prime that contains the beastly number '666' and begins and ends with digit 1.
a(2) = 1000000000000066600000000000001 is palindromic prime that contains the beastly number '666' and begins and ends with digit 1.

Links

Crossrefs

Cf. A046720, A051003, A131645, A186086.

Programs

  • Magma
    [k: n in [1..1000] | IsPrime(k) where k is ((1*10^(n + 2) + 666)*10^n + 1 )];
  • Maple
    A260312:= n-> ((1*10^(n + 2) + 666)*10^n + 1 ): select(isprime, [seq((A260312 (n), n=1..100))]);
  • Mathematica
    Select[Table[(1*10^(n + 2) + 666)*10^n + 1, {n, 1000}], PrimeQ]
Select[Table[FromDigits[Join[{1},PadRight[{},n,0],{6,6,6},PadRight[ {},n,0],{1}]],{n,0,50}],PrimeQ] (* Harvey P. Dale, Jul 09 2017 *)
  • PARI
    for(n=1, 500, k=((1*10^(n + 2) + 666)*10^n + 1 ); if(isprime(k), print1(k, ", ")));
Showing 1-5 of 5 results.

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