A006567 -id:A006567 - cp's OEIS frontend

A352249 Emirps that can be written as p*q+p+q where p and q are emirps.

1439, 1511, 3023, 14447, 16127, 16547, 16883, 19763, 30059, 33623, 35099, 35327, 36251, 38219, 39359, 72911, 75239, 76463, 78623, 94559, 96431, 100799, 103511, 107603, 108191, 108863, 110807, 118583, 119039, 119363, 120539, 121727, 126359, 127679, 128879, 129959, 132299, 132887, 134999, 136403

Offset: 1

J. M. Bergot and Robert Israel, Apr 17 2022

			a(3) = 3023 is a term because 3023 = 17*167+17+167 and 3023, 17 and 167 are emirps.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A006567.

revdigs:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:
isemirp:= proc(p) local r;
   if not isprime(p) then return false fi;
   r:= revdigs(p);
   r <> p and isprime(r)
end proc:
E:= select(isemirp, [seq(ithprime(i),i=1..10^4)]):
nE:= nops(E): N:= E[1]*E[-1]+E[1]+E[-1]:
S:= {}:
for i from 1 to nE do
  for j from i+1 to nE do
    x:= E[i]*(E[j]+1)+E[j];
    if x > N then break fi;
    if isemirp(x) then S:= S union {x} fi;
od od:
sort(convert(S,list));

A040104 First ten consecutive primes which are emirps.

Original entry on oeis.org

1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259

Offset: 1

Carlos Rivera

There are no additional such ten-consecutive primes up through the 3 millionth prime (49,979,687). - Harvey P. Dale, May 20 2014

Carlos Rivera, Problem 17. The largest known sequence of consecutive and reversible primes, The Prime Puzzles and Problems Connection.
Carlos Rivera, Puzzle 20. Reversible Primes, The Prime Puzzles and Problems Connection.

Cf. A006567, A048051, A048052, A103172.

Flatten[Select[Partition[Prime[Range[220]],10,1],And@@PrimeQ[ FromDigits/@ (Reverse/@(IntegerDigits/@#))]&]] (* Harvey P. Dale, May 20 2014 *)

New name from Charles R Greathouse IV, Jan 13 2014

A071614 a(n) is the smallest emirp that is the first of n consecutive emirps with equal digit sum.

Original entry on oeis.org

13, 79, 15919, 197837, 3528871, 110539181, 731854429, 9819391129

Offset: 1

Klaus Brockhaus, May 27 2002

a(9) > 10^11. - Donovan Johnson, Nov 07 2010

			a(3) = 15919, since 15919,15937,15973 are three consecutive emirps with digit sum 25 and this is the first occurrence of three consecutive emirps with equal digit sum.

Cf. A006567, A070905, A071612, A071613.

a(7)-a(8) from Donovan Johnson, Nov 07 2010

A109019 Numbers whose digit reversal is different and has the same number of prime factors (with multiplicity).

Original entry on oeis.org

13, 15, 17, 26, 31, 37, 39, 49, 51, 58, 62, 71, 73, 79, 85, 93, 94, 97, 107, 113, 115, 117, 122, 123, 126, 129, 143, 147, 149, 155, 157, 158, 159, 165, 167, 169, 177, 178, 179, 183, 185, 187, 199, 203, 205, 221, 225, 226, 244, 246, 265, 270, 285, 286, 289, 290

Offset: 1

Jonathan Vos Post, Jun 16 2005

Ray Chandler has coauthorship credit for this sequence.

Eric Weisstein's World of Mathematics, Almost Prime.
Eric Weisstein's World of Mathematics, Emirp.
Eric Weisstein's World of Mathematics, Emirpimes.

Cf. A006567, A097393, A109018, A109023-A109031.

Select[Range@1000, ! PalindromeQ@# && Differences@PrimeOmega@{#,IntegerReverse@#} == {0} &] (* Hans Rudolf Widmer, Jun 03 2022 *)

{A006567} U {A097393} U {A109023} U {A109024} U ... U {A109031} U ...

More terms from Stefan Steinerberger, Jun 16 2007

A127746 Smallest n-digit prime whose reversal is also prime.

Original entry on oeis.org

2, 13, 107, 1009, 10007, 100049, 1000033, 10000169, 100000007, 1000000007, 10000000207, 100000000237, 1000000000091, 10000000000313, 100000000000261, 1000000000000273, 10000000000000079, 100000000000000049

Offset: 1

Lekraj Beedassy, Jan 28 2007

Smallest n-digit emirp (A006567).
Largest n-digit emirp is given by A114019.
Least emirp (A006567) greater than 10^(n-1). [Jonathan Vos Post, Nov 15 2009]
Palindromes not permitted (with the exception of the first term), so for example 101 is not a term. - Harvey P. Dale, Mar 11 2017

Harvey P. Dale, Table of n, a(n) for n = 1..100

Cf. A006567, A031991, A114019, A114018, A127747.

Cf. A000040, A004086, A007500. [Jonathan Vos Post, Nov 15 2009]

f[n_] := Block[{k = 10^(n - 1), id, rid}, While[ id = IntegerDigits[k]; rid = Reverse[id]; ! PrimeQ[k] || ! PrimeQ[FromDigits[rid]] || id == rid, k++ ]; k]; Table[f[n], {n, 2, 19}] (* Ray Chandler, Jan 30 2007 *)
sndp[n_]:=Module[{np=NextPrime[10^(n+1)]},While[PalindromeQ[np] || !PrimeQ[ IntegerReverse[ np]],np= NextPrime[np]];np]; Join[{2},Array[sndp,20,0]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 11 2017 *)

Edited and extended by Ray Chandler, Jan 30 2007

A128374 Emirps starting and ending with composite digit 9.

Original entry on oeis.org

9029, 9209, 9349, 9439, 9479, 9679, 9749, 9769, 90019, 90059, 90089, 90149, 90199, 90499, 90679, 90749, 90989, 91009, 91129, 91199, 91229, 91249, 91459, 92119, 92189, 92219, 92369, 92459, 92479, 92489, 92639, 92779, 92789, 92899, 92959

Offset: 1

Lekraj Beedassy, Feb 27 2007

Cf. A006567, A128375.

Corrected and extended by Ray Chandler, Feb 28 2007

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

Lekraj Beedassy, Feb 28 2007

Subsequence of A128374.

Cf. A006567, A128388, A128390.

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

Extended by Ray Chandler, Mar 06 2007

A143260 Primes that are not emirps.

Original entry on oeis.org

2, 3, 5, 7, 11, 19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 101, 103, 109, 127, 131, 137, 139, 151, 163, 173, 181, 191, 193, 197, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 313, 317, 331, 349, 353, 367, 373, 379, 383

Offset: 1

Lekraj Beedassy, Aug 02 2008

Complement of A006567 with respect to A000040.

Select[Prime[Range[100]],PalindromeQ[#]||!PrimeQ[IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 29 2017 *)

A152014 Number of n-digit primes whose reversal is a different prime.

Original entry on oeis.org

0, 8, 28, 204, 1406, 9538, 70474, 535578, 4192024, 33619380, 274890230, 2294771254

Offset: 1

Zak Seidov, Nov 19 2008

All terms are even.

			a(1)=0 because there are no 1-digit terms in A006567.
a(2)=8 because there are eight 2-digit terms in A006567: 13,17,31,37,71,73,79,97.

Cf. A006567.

Do[c = 0; p = NextPrime[10^(n - 1) - 1]; n1 = PrimePi[p]; n2 = PrimePi[NextPrime[10^n, -1]] - n1 + 1; Do[id = IntegerDigits[p]; i1 = id[[1]]; If[OddQ[i1] && i1 != 5, p1 = FromDigits[ Reverse[id]]; If[p1 != p, If[PrimeQ[p1], c++ ]]]; p = NextPrime[p], {n2}]; Print[{n, c}], {n, 1, 9}];

a(10)-a(11) from Donovan Johnson, Nov 01 2010

a(12) from Lars Blomberg, Jun 28 2021

A152034 a(n) = largest n-digit prime p whose reversal is a prime q > p.

Original entry on oeis.org

79, 769, 9679, 98999, 995699, 9975899, 99967999, 999548999, 9999049999, 99994169999, 999989299999, 9999954799999, 99999904999999, 999999778999999, 9999999349999999, 99999994999999999, 999999971189999999, 9999999950999999999, 99999999632999999999

Offset: 2

Zak Seidov, Nov 20 2008

Robert Israel, Table of n, a(n) for n = 2..200

Cf. A006567, A152014, A152033.

revdigs:= proc(x) local L,i; L:= convert(x,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:
f:= proc(n)
  local d,a,B,r;
  for d from floor(n/2) by -1 do
     B:= (10^d-1)*(1+10^(n-d));
     for a from 10^(n-2*d)-1 to 1 by -1 do
       r:= revdigs(a);
       if r > a and isprime(B+10^d*a) and isprime(B+10^d*r) then return B+10^d*a fi
     od
  od
end proc:
map(f, [$2..20]); # Robert Israel, Aug 16 2016

Do[ p = NextPrime[10^(n ), -1 ]; Do[ p1 = FromDigits[ Reverse[IntegerDigits[p]]]; If[PrimeQ[p1] && p1 > p, Print[{n, p}]; Break[]]; p = NextPrime[p, -1], {10^9}], {n, 2, 15}];

More terms from Max Alekseyev, May 03 2011

cp's OEIS Frontend

A352249 Emirps that can be written as p*q+p+q where p and q are emirps.

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A040104 First ten consecutive primes which are emirps.

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A071614 a(n) is the smallest emirp that is the first of n consecutive emirps with equal digit sum.

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A109019 Numbers whose digit reversal is different and has the same number of prime factors (with multiplicity).

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Mathematica

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A127746 Smallest n-digit prime whose reversal is also prime.

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Mathematica

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A128374 Emirps starting and ending with composite digit 9.

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

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A143260 Primes that are not emirps.

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Mathematica

A152014 Number of n-digit primes whose reversal is a different prime.

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Mathematica