cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Omar E. Pol, Mar 25 2008

Keywords

Comments

Subset of A138126.
Note that all members, in base 10, contain the digit 7 and do not contains the digit 9.
All members of A054356 (The Five Hysterical Girls Theorem) are prime numbers.

Examples

			A000040(471) ....... = 3343
A000040(3570) ...... = 33343
A000040(28674) ..... = 333433
A000040(28743) ..... = 334333
A000040(13077233344) = 333333433343
		

Crossrefs

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

Views

Author

Keywords

Crossrefs

Cf. A054356.

Programs

  • Magma
    [p: p in PrimesUpTo(43444433) | Set(Intseq(p)) subset [3,4]];
    // Bruno Berselli, Jul 27 2012
  • Mathematica
    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

Views

Author

Arkadiusz Wesolowski, Mar 15 2016

Keywords

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.

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 *)

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

Views

Author

Omar E. Pol, Mar 25 2008

Keywords

Comments

Indices of A054356 (The Five Hysterical Girls Theorem) are members of this sequence (See A138132).

Examples

			a(5)=471 because A020461(5)=3343 and A000040(471)=3343, the 471st prime number.
		

Crossrefs

Showing 1-4 of 4 results.