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 1-8 of 8 results.

A133753 Larger of emirps (pairs) with only prime digits (A128388).

Original entry on oeis.org

73, 733, 3733, 7253, 7523, 7757, 33223, 35323, 72253, 72353, 73327, 73523, 73553, 75223, 75253, 77237, 77323, 77527, 77557, 333323, 352333, 355723, 375223, 375233, 375553, 722333, 727327, 733333, 735733, 737353, 737753, 737773, 753373, 753527, 772273, 773273, 775757, 777353, 777373
Offset: 1

Views

Author

Lekraj Beedassy, Jan 21 2008

Keywords

Links

Crossrefs

Cf. A128388, A133554.

Programs

  • Maple
    read(transforms) : isA006567 := proc(n) local digs,prev ; if isprime(n) then prev := digrev(n) ; if n <> prev and isprime(prev) then true ; else false ; fi ; else false ; fi ; end: isA128388 := proc(n) local digs ; if isA006567(n) then digs := convert(convert(n,base,10),set) ; if digs minus {2,3,5,7} = {} then true ; else false ; fi ; else false ; fi ; end: isA133753 := proc(n) if isA128388(n) then if digrev(n) < n then true; else false ; fi ; else false ; fi ; end: for n from 1 to 200000 do p := ithprime(n) ; if isA133753(p) then printf("%d, ",p) ; fi ; od: # R. J. Mathar, Jan 30 2008
  • Mathematica
    Select[(Table[(Sort/@Select[{#,IntegerReverse[#]}&/@Select[FromDigits/@Tuples[ {2,3,5,7},n],PrimeQ],AllTrue[#,PrimeQ]&])[[;;,2]]//Union,{n,2,6}]//Flatten//Union),!PalindromeQ[#]&] (* Harvey P. Dale, Sep 15 2024 *)

Formula

{p in A128388: p> A004086(p)}. - R. J. Mathar, Jan 30 2008

Extensions

Extended by Ray Chandler and R. J. Mathar, Jan 30 2008

A133554 Lesser of emirps (pairs) with only prime digits (A128388).

Original entry on oeis.org

37, 337, 3257, 3373, 3527, 7577, 32233, 32257, 32353, 32377, 32537, 35227, 35257, 35327, 35537, 72337, 72577, 73277, 75577, 322573, 323333, 327553, 332573, 333227, 333253, 333337, 337537, 353737, 353777, 355573, 357737, 372277, 372377, 373357, 373777, 377737, 723727, 725357, 757577
Offset: 1

Views

Author

Lekraj Beedassy, Jan 21 2008

Keywords

Crossrefs

Cf. A128388, A133753.

Extensions

Extended by Ray Chandler, Jan 30 2008

A128390 Emirps with only nonprime digits (i.e., 0, 1, 4, 6, 8, 9).

Original entry on oeis.org

149, 199, 941, 991, 1009, 1061, 1069, 1091, 1109, 1181, 1409, 1499, 1601, 1619, 1669, 1811, 1901, 1949, 9001, 9011, 9041, 9161, 9491, 9601, 9661, 9941, 10009, 10061, 10069, 10091, 10499, 10889, 10891, 10909, 11149, 11161, 11489, 11699, 11909
Offset: 1

Views

Author

Lekraj Beedassy, Feb 28 2007

Keywords

Crossrefs

Cf. A006567, A128388, A128389.

Programs

  • Mathematica
    Select[Prime@Range@(10^4), (r = IntegerReverse@#) != # && PrimeQ@r && Intersection[IntegerDigits@#, {2, 3, 5, 7}] == {} &] (* Ray Chandler, Mar 06 2007 corrected by Hans Rudolf Widmer, May 18 2024 *)

Extensions

Corrected by Ray Chandler, Mar 06 2007

A177513 Smallest n-digit emirp with only prime digits.

Original entry on oeis.org

37, 337, 3257, 32233, 322573, 3223357, 32235223, 322222757, 3222222257, 32222232577, 322222232537, 3222222223333, 32222222332733, 322222222237537, 3222222222223373, 32222222222223353, 322222222222225333
Offset: 2

Views

Author

Lekraj Beedassy, May 10 2010

Keywords

Comments

Palindromes are not permitted. - Harvey P. Dale, Jun 12 2016

Crossrefs

Cf. A177514, A128388

Extensions

a(8) corrected and a(11)-a(18) from Donovan Johnson, Jul 30 2010

A128389 Emirps with only composite digits (i.e., 4, 6, 8, 9).

Original entry on oeis.org

94889, 98849, 98999, 99989, 946949, 949649, 9446989, 9464849, 9466949, 9468869, 9468989, 9484649, 9489899, 9494689, 9496649, 9648889, 9666689, 9688649, 9689689, 9699889, 9844699, 9844889, 9846989, 9864889, 9864949, 9866669
Offset: 1

Views

Author

Lekraj Beedassy, Feb 28 2007

Keywords

Comments

Subsequence of A128374.

Crossrefs

Cf. A006567, A128388, A128390.

Programs

  • Mathematica
    Select[Prime@Range[10^6], # != r[ # ] && PrimeQ[r[ # ]] && Intersection[IntegerDigits[ # ], {0, 1, 2, 3, 5, 7}] == {} &] (* Ray Chandler, Mar 06 2007 *)

Extensions

Extended by Ray Chandler, Mar 06 2007

A137833 Emirps with a prime number of only prime digits.

Original entry on oeis.org

37, 73, 337, 733, 32233, 32257, 32353, 32377, 32537, 33223, 35227, 35257, 35323, 35327, 35537, 72253, 72337, 72353, 72577, 73277, 73327, 73523, 73553, 75223, 75253, 75577, 77237, 77323, 77527, 77557, 3223357, 3223537, 3225323, 3225737
Offset: 1

Views

Author

Lekraj Beedassy, Feb 12 2008

Keywords

Links

Crossrefs

Cf. A137834, A137835.

Programs

  • Mathematica
    Select[Prime@Range[235000], # != IntegerReverse[ # ] && PrimeQ[IntegerReverse[ # ]] && ContainsOnly[IntegerDigits[ # ], {2,3,5,7}] &&PrimeQ[IntegerLength[#]]&] (* James C. McMahon, Jun 03 2025 *)
Table[Select[FromDigits/@Tuples[{2,3,5,7},p],!PalindromeQ[#]&&AllTrue[{#,IntegerReverse[#]},PrimeQ]&],{p,Prime[Range[4]]}]//Flatten (* Harvey P. Dale, Aug 02 2025 *)

Formula

Subsequence of A128388.

Extensions

More terms from Sean A. Irvine, Mar 23 2010

A137836 Emirps using only and all of the prime digits 2,3,5,7.

Original entry on oeis.org

3257, 3527, 7253, 7523, 32257, 32537, 35227, 35257, 35327, 72253, 72353, 73523, 75223, 75253, 322573, 327553, 332573, 355723, 375223, 375233, 725357, 753527, 3223357, 3223537, 3225737, 3235577, 3235777, 3237527, 3252377, 3253753
Offset: 1

Views

Author

Lekraj Beedassy, Feb 12 2008

Keywords

Links

Crossrefs

Subsequence of A128388.

Programs

  • Maple
    read transforms : isA006567 := proc(n) local nrev ; if isprime(n) then nrev := digrev(n) ; nrev <> n and isprime(nrev)) ; else false ; fi ; end: isA137836 := proc(n) local dgs ; if isA006567(n) then dgs := convert(convert(n,base,10),set) ; if dgs minus {2,3,5,7} <> {} then false ; elif nops(dgs) <> 4 then false ; else true ; fi ; else false ; fi ; end: for n from 1 to 1000000 do p := ithprime(n) ; if isA137836(p) then print(p) ; fi ; od: # R. J. Mathar, Feb 28 2008
  • Mathematica
    Take[With[{nn=2},Union[FromDigits/@Select[Select[Flatten[Permutations/@ Flatten[ Table[Join[{2,3,5,7},Table[2,{i}],Table[3,{j}],Table[5,{k}], Table[7,{l}]],{i,0,nn},{j,0,nn},{k,0,nn},{l,0,nn}],3],1], PrimeQ[ FromDigits[#]]&], PrimeQ[FromDigits[Reverse[#]]]&]]],100] (* Harvey P. Dale, Nov 07 2012 *)

Extensions

Corrected and extended by R. J. Mathar, Feb 28 2008

A177514 Largest n-digit emirp with only prime digits.

Original entry on oeis.org

73, 733, 7757, 77557, 777373, 7777573, 77757553, 777777373, 7777777237, 77777773537, 777777777773, 7777777777573, 77777777772257, 777777777752557, 7777777777752757, 77777777777753233, 777777777777753553
Offset: 2

Views

Author

Lekraj Beedassy, May 10 2010

Keywords

Crossrefs

Cf. A177514, A128388

Extensions

a(8) and a(9) corrected and a(11)-a(18) from Donovan Johnson, Jul 30 2010
Showing 1-8 of 8 results.

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