A138132
Indices among the primes of the primes in A054356, The Five Hysterical Girls Theorem.
Original entry on oeis.org
471, 3570, 28674, 28743, 13077233344
Offset: 1
A000040(471) ....... = 3343
A000040(3570) ...... = 33343
A000040(28674) ..... = 333433
A000040(28743) ..... = 334333
A000040(13077233344) = 333333433343
A020461
Primes that contain digits 3 and 4 only.
Original entry on oeis.org
3, 43, 433, 443, 3343, 3433, 33343, 333433, 334333, 343333, 343433, 444343, 444443, 3333433, 3343343, 3343433, 3344333, 3344443, 3433333, 3434443, 3443443, 3444443, 4344443, 4433333, 4434343, 4443433, 34333333, 34434343, 34444343, 43444433
Offset: 1
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[p: p in PrimesUpTo(43444433) | Set(Intseq(p)) subset [3,4]];
// Bruno Berselli, Jul 27 2012
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Flatten[Table[Select[FromDigits/@Tuples[{3,4},n],PrimeQ],{n,8}]] (* Vincenzo Librandi, Jul 27 2012 *)
A270338
Primes whose decimal expansion contains only 3's and 4's, in which every 4 is preceded and followed by a 3.
Original entry on oeis.org
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
- Giorgio Balzarotti, Paolo P. Lava, Centotre curiosità matematiche, Hoepli, 2010, pp. 3-4.
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[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)];
-
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
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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 *)
A138126
Indices among the primes of the primes in A020461.
Original entry on oeis.org
2, 14, 84, 86, 471, 481, 3570, 28674, 28743, 29448, 29457, 37293, 37299, 239128, 239793, 239800, 239852, 239864, 245780, 245859, 246469, 246541, 305733, 311548, 311615, 312235, 2108429, 2114208, 2114772, 2629825
Offset: 1
a(5)=471 because A020461(5)=3343 and A000040(471)=3343, the 471st prime number.
Showing 1-4 of 4 results.
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