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.

A153806 Strobogrammatic cyclops numbers.

Original entry on oeis.org

0, 101, 609, 808, 906, 11011, 16091, 18081, 19061, 61019, 66099, 68089, 69069, 81018, 86098, 88088, 89068, 91016, 96096, 98086, 99066, 1110111, 1160911, 1180811, 1190611, 1610191, 1660991, 1680891, 1690691, 1810181, 1860981
Offset: 1

Views

Author

Omar E. Pol, Jan 15 2009

Keywords

Comments

Intersection of A000787 and A134808.

Examples

			1680891 is a member because it is the same upside down (A000787) and also a cyclops number (A134808).

Links

Crossrefs

Cf. A000787, A007597, A134808, A134809, A138131, A138148, A153807.

Programs

  • Mathematica
    Select[Range[10^7], And[OddQ@ Length@#, Part[#, Ceiling[Length[#]/2]] == 0, Times @@ Boole@ Map[MemberQ[{0, 1, 6, 8, 9}, #] &, Union@ #] == 1, Count[#, 0] == 1, (Take[#, Floor[Length[#]/2]] /. {6 -> 9, 9 -> 6}) ==
Reverse@ Take[#, -Floor[Length[#]/2]]] &@ IntegerDigits@ # &] (* Michael De Vlieger, Jul 05 2016 *)
  • Python
    import sys
f = open('b153806.txt', 'w')
i = 1
n = 0
a = [""]
r = [""]  #reversed strobogrammatically
while True:
    for x,y in zip(a,r):
        f.write(str(i)+" "+x+"0"+y+"\n")
        i += 1
        if i>20000:
            f.close()
            sys.exit()
    a = sum([[x+"1",x+"6",x+"8",x+"9"] for x in a],[])
    r = sum([["1"+x,"9"+x,"8"+x,"6"+x] for x in r],[])
# Kenny Lau, Jul 05 2016

Extensions

Extended beyond 11011 by R. J. Mathar, Jan 17 2009

A160561 Cyclops primes with circular digits {0,6,8,9}.

Original entry on oeis.org

809, 66089, 68099, 86069, 88069, 89069, 99089, 6680689, 6680699, 6680969, 6690689, 6690899, 6690989, 6860869, 6860989, 6860999, 6890699, 6890969, 6960869, 6980669, 6980899, 6980969, 6990889, 8660689, 8660699, 8660969
Offset: 1

Views

Author

Ki Punches, May 19 2009

Keywords

Comments

The sequence is probably infinite.
The sequence A134809 restricted to cases with digits 6, 8 or 9 (see A001743) at the off-center positions.
Primes in A274765. - Omar E. Pol, Jul 06 2016
Each term is equal to 9 mod 10. - Harvey P. Dale, Feb 02 2021

Links

Crossrefs

Intersection of A000040 (primes), A001743 (numbers with circular digits) and A134808 (cyclops numbers).
Also intersection of A043580 (primes with circular digits) and A134809 (cyclops primes).
Cf. A134808, A134809, A153807, A156200, A274765.

Programs

  • Mathematica
    Select[Prime@ Range[10^6], And[OddQ@ Length@ #, Times @@ Boole@ Map[MemberQ[{0, 6, 8, 9}, #] &, Union@ #] == 1, Part[#, Ceiling[Length[#]/2]] == 0, Count[#, 0] == 1] &@ IntegerDigits@ # &] (* Michael De Vlieger, Jul 05 2016 *)
Table[Select[FromDigits/@(Flatten[Join[{Take[#,Length[#]/2],0,Take[#,-Length[#]/2]}]]&/@Tuples[{6,8,9},n]),PrimeQ],{n,2,6,2}]//Flatten (* Harvey P. Dale, Feb 02 2021 *)

Extensions

Edited and corrected by Ray Chandler and R. J. Mathar, May 20 2009
Definition simplified by Omar E. Pol, Jun 05 2009

A160725 Cyclops semiprimes.

Original entry on oeis.org

106, 201, 202, 203, 205, 206, 209, 301, 302, 303, 305, 309, 403, 407, 501, 502, 505, 703, 706, 707, 802, 803, 807, 901, 905, 11013, 11014, 11015, 11017, 11019, 11021, 11023, 11029, 11031, 11035, 11038, 11041, 11042, 11051, 11053
Offset: 1

Views

Author

Omar E. Pol, Jun 12 2009

Keywords

Comments

Cyclops numbers (A134808) that are also semiprimes (A001358).

Links

Crossrefs

Cf. A001358, A134808, A134809, A138131, A138148, A153806, A153807, A160711, A160712, A160717.

Programs

  • Maple
    g:= proc(x,n)
  local L,i;
  L:= convert(x+9^(2*n),base,9);
  add((L[i]+1)*10^(i-1),i=1..n)+add((L[i]+1)*10^i,i=n+1..2*n)
end proc:
select(t -> numtheory:-bigomega(t)=2,[seq(seq(g(i,n),i=0..9^(2*n)-1),n=1..2)]); # Robert Israel, Jan 20 2019
  • Mathematica
    Select[Range@ 12000, And[OddQ@ #2, #3[[Ceiling[#2/2] ]] == 0, Count[#3, 0] == 1, PrimeOmega@ #1 == 2] & @@ {#, IntegerLength@ #, IntegerDigits@ #} &] (* or *)
Select[Flatten@ Table[a (10^(d + 1)) + b, {d, 2}, {a, FromDigits /@ Tuples[Range@ 9, {d}]}, {b, FromDigits /@ Tuples[Range@ 9, {d}]}], PrimeOmega@ # == 2 &] (* Michael De Vlieger, Jan 20 2019 *)

A183058 Cyclops Sophie-Germain primes.

Original entry on oeis.org

509, 809, 12011, 12041, 13049, 14081, 16091, 18041, 21011, 21089, 22013, 22079, 23099, 25073, 28019, 29021, 29033, 31019, 33023, 33053, 35069, 35081, 35099, 36083, 37013, 37049, 38039, 39089, 41081, 42023, 42071, 42089, 43013
Offset: 1

Views

Author

Omar E. Pol, Dec 26 2010

Keywords

Comments

Sophie Germain primes which are also Cyclops numbers.

Examples

			509 is in the sequence because 509 is a Sophie Germain prime A005384 and it is also a Cyclops number A134808.

Links

Crossrefs

Cf. A005384, A134808, A134809, A136098, A153807, A183059.

Programs

  • Maple
    isA005384 := proc(n) isprime(n) and isprime(2*n+1) ; end proc:
isA134808 := proc(n) local dgs,ndgs; dgs := convert(n,base,10) ; mdg := (nops(dgs)+1)/2 ; if type(nops(dgs),'even') then false; elif n = 0 then true; else if op(mdg,dgs) <> 0 then false; else if mul(op(k,dgs),k=1..mdg-1) =0 or mul(op(k,dgs),k=mdg+1..nops(dgs)) = 0 then false; else true; end if; end if; end if; end proc:
isA183058 := proc(n) isA005384(n) and isA134808(n) ; end proc:
for n from 0 to 50000 do if isA183058(n) then printf("%d,",n); end if; end do: # R. J. Mathar, Jan 05 2011
  • Mathematica
    csgpQ[n_]:=Module[{idn=IntegerDigits[n],len},len=Length[idn];PrimeQ[2n+1]&&OddQ[len]&&idn[[(len+1)/2]]==0&&Count[idn,0]==1]; Select[Prime[ Range[ 4500]],csgpQ] (* Harvey P. Dale, Jun 06 2020 *)

Formula

A005384 INTERSECT A134808.
Showing 1-4 of 4 results.

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