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 1-6 of 6 results.

A128388 Emirps with only prime digits (i.e., 2, 3, 5, 7).

Original entry on oeis.org

37, 73, 337, 733, 3257, 3373, 3527, 3733, 7253, 7523, 7577, 7757, 32233, 32257, 32353, 32377, 32537, 33223, 35227, 35257, 35323, 35327, 35537, 72253, 72337, 72353, 72577, 73277, 73327, 73523, 73553, 75223, 75253, 75577, 77237, 77323
Offset: 1

Views

Author

Lekraj Beedassy, Feb 28 2007

Keywords

Comments

7523 is the largest norep emirp with only prime digits. - Harvey P. Dale, Sep 17 2019

Links

Crossrefs

Cf. A006567, A128389, A128390.

Programs

  • Mathematica
    Select[Prime@Range[10^4], # != IntegerReverse[ # ] && PrimeQ[IntegerReverse[ # ]] && Intersection[IntegerDigits[ # ], {0, 1, 4, 6, 8, 9}] == {} &] (* Ray Chandler, Mar 06 2007; corrected by James C. McMahon, Jun 03 2025 *)
Table[Select[FromDigits/@Tuples[{2,3,5,7},n],!PalindromeQ[#]&& AllTrue[ {#, IntegerReverse[ #]},PrimeQ]&],{n,2,5}]//Flatten (* Requires Mathematica version 10 or later *)  (* Harvey P. Dale, Sep 17 2019 *)

Extensions

Corrected by Ray Chandler, Mar 06 2007

A155512 Emirps with digits 0 and 1 only.

Original entry on oeis.org

10011101, 10111001, 100100111, 111001001, 1000110101, 1001001011, 1010001101, 1010011111, 1010110001, 1011000101, 1101001001, 1111100101, 10010100101, 10100000011, 10100000111, 10100101001, 10111001011, 11000000101
Offset: 1

Views

Author

Lekraj Beedassy, Jan 23 2009

Keywords

Comments

Subsequence of A128390 and of A020449.

Links

Crossrefs

A006567, A155513, A155514

Programs

  • Mathematica
    emQ[ls_List]:=Module[{rev=Reverse[ls]},Length[ls]==Length[rev]&& ls!=rev && PrimeQ[FromDigits[ls]]&&PrimeQ[FromDigits[rev]]]; Union[Flatten[ Table[FromDigits/@Select[Tuples[{1,0},n],emQ],{n,11}]]] (* Harvey P. Dale, Nov 30 2011 *)

Extensions

First two missed entries included. Lekraj Beedassy, May 30 2009
More terms from Sean A. Irvine, Mar 04 2010

A155507 Emirps with digits 1 and 9 only.

Original entry on oeis.org

199, 991, 91199, 99119, 111119, 111919, 119191, 191911, 911111, 919111, 991999, 999199, 1191119, 1191191, 1191991, 1911911, 1991911, 9111911, 11111911, 11191991, 11911111, 11919991, 19111991, 19911191, 19919111, 19991911
Offset: 1

Views

Author

Lekraj Beedassy, Jan 23 2009

Keywords

Comments

Subsequence of A128390.

Links

Crossrefs

A006567, A128390, A155508, A155509

Programs

  • Mathematica
    emrpQ[n_]:=Module[{r=IntegerReverse[n]},r!=n&&AllTrue[{r,n},PrimeQ]]; Table[Select[FromDigits/@Tuples[{1,9},n],emrpQ],{n,8}]//Flatten (* Harvey P. Dale, Aug 09 2017 *)

Extensions

More terms from Sean A. Irvine, Apr 05 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

A157533 Emirps using all nonprime digits (0, 1, 4, 6, 8, 9) and no others.

Original entry on oeis.org

108649, 140869, 168409, 184609, 904861, 906481, 946801, 968041, 1016489, 1041869, 1048609, 1061849, 1064689, 1068409, 1068491, 1084469, 1084609, 1086469, 1089461, 1098469, 1108469, 1146809, 1184069, 1406689, 1406849, 1408619, 1408699, 1460089, 1460189, 1460981
Offset: 1

Views

Author

Lekraj Beedassy, Mar 02 2009

Keywords

Comments

Subsequence of A128390.

Links

Crossrefs

Cf. A128390.
Cf. A006567 (emirps, primes whose reversal is a different prime). - Klaus Brockhaus, Mar 08 2009

Programs

  • Magma
    [ n : n in [100000..1410000] | Seqset(D) eq {0, 1, 4, 6, 8, 9}and n ne r and IsPrime(n) and IsPrime(r) where r is Seqint(Reverse(D)) where D is Intseq(n) ]; // Klaus Brockhaus, Mar 08 2009
  • Mathematica
    Select[Prime[Range[300000]],Union[IntegerDigits[#]]=={0,1,4,6,8,9}&&PrimeQ[IntegerReverse[#]]&&#!=IntegerReverse[#]&] (* K. D. Bajpai, Jan 11 2020 *)

Extensions

Edited by N. J. A. Sloane, Mar 05 2009
More terms from Klaus Brockhaus and Ray Chandler, Mar 08 2009

A177850 Smallest n-digit emirp with only nonprime digits.

Original entry on oeis.org

149, 1009, 10009, 100049, 1000849, 10000169, 100000891, 1000000009, 10000001041, 100000000669, 1000000000091, 10000000001011, 100000000000469, 1000000000004449, 10000000000001101, 100000000000000049
Offset: 3

Views

Author

Jonathan Vos Post, May 14 2010

Keywords

Comments

Least value of emirps with only nonprime digits (i.e., 0,1,4,6,8,9) A128390, with n digits. This is to primes with nonprime digits (A034844) as smallest n-digit emirp with only prime digits (A177513) is to primes with only prime digits.

Examples

			a(6) = 100049 because all digits {0,1,4,9} are nonprime, and 100049 is prime, and R(100049) = A004086(100049) = 940001 is prime, and there is no smaller 6-digit number meeting these criteria.

Crossrefs

Cf. A000040, A004086, A006567, A034844, A128390, A177513.

Programs

  • Maple
    isA084984 := proc(n) convert(convert(n,base,10),set) ; if % intersect {2,3,5,7} = {} then true; else false; end if; end proc:
A177850 := proc(n) local a; a := 10^(n-1) ; while not (isA006567(a) and isA084984(a)) do a := nextprime(a) ; end do; if a < 10^n then return a ; else return -1 ; end if; end proc:
seq(A177850(n),n=3..40) ; # R. J. Mathar, May 24 2010

Extensions

More terms from R. J. Mathar, May 24 2010
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.