A270338 Primes whose decimal expansion contains only 3's and 4's, in which every 4 is preceded and followed by a 3.

3343, 3433, 33343, 333433, 334333, 343333, 343433, 3333433, 3343343, 3343433, 3433333, 34333333, 333334333, 333343343, 333343433, 333433343, 333434333, 334334333, 3333334343, 3333433343, 3334333333, 3343334333, 3343434343, 3433434343, 3434343433, 33333333343

Offset: 1

Author

Arkadiusz Wesolowski, Mar 15 2016

Keywords

• nonn
• base
• dumb

Comments

A sequence related to A054356. These primes look like "EEhEEhEEE" when viewed upside down by rotation of 180 degrees (3343 - "EhEE", 3433 - "EEhE", 33343 - "EhEEE", 333433 - "EEhEEE").

References

• Giorgio Balzarotti, Paolo P. Lava, Centotre curiosità matematiche, Hoepli, 2010, pp. 3-4.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!: 47
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!: 3343

Crossrefs

Cf. A054356. Subsequence of A020461.

Programs

Magma

[p: p in [3..33333333343 by 10] | (p mod 100 eq 33 or p mod 100 eq 43) and IsPrime(p) and Position(IntegerToString(p), IntegerToString(3)) eq 1 and Set(Intseq(p)) subset [3, 4] and not IntegerToString(44) in IntegerToString(p)];

Maple

S:= {}:
for n from 3 to 16 do
  for k from 1 to floor((n-1)/2) do
     for r in combinat:-choose(n-1-k,k) do
        L:=subsop(seq(t=(3,4),t=r),[3$(n-k)]);
        x:= add(L[i]*10^(n-i),i=1..n);
        if isprime(x) then S:= S union {x} fi
od od od:
sort(convert(S,list)); # Robert Israel, Mar 15 2016

Mathematica

Select[Flatten[Table[FromDigits/@Select[Tuples[{3,4},n],SequenceCount[ #,{3,4,3},Overlaps->True]==Count[#,4]&],{n,3,11}]],PrimeQ]//Sort (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 17 2016 *)