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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 (list; graph; refs; listen; history; text; internal format)
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

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

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 A255731 A204884

Adjacent sequences:  A270335 A270336 A270337 * A270339 A270340 A270341

KEYWORD

nonn,base,dumb

AUTHOR

Arkadiusz Wesolowski, Mar 15 2016

STATUS

approved

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Last modified January 28 06:59 EST 2021. Contains 340490 sequences. (Running on oeis4.)