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A270338
Primes whose decimal expansion contains only 3's and 4's, in which every 4 is preceded and followed by a 3.
2
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
1,1
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
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!: 47
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!: 3343
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 *)
PROG
(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)];
CROSSREFS
Cf. A054356. Subsequence of A020461.
Sequence in context: A231955 A255657 A252188 * A054356 A358312 A348525
KEYWORD
nonn,base,dumb
AUTHOR
STATUS
approved