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.

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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

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 *)

A386340 Primes without {3, 4} as digits.

Original entry on oeis.org

2, 5, 7, 11, 17, 19, 29, 59, 61, 67, 71, 79, 89, 97, 101, 107, 109, 127, 151, 157, 167, 179, 181, 191, 197, 199, 211, 227, 229, 251, 257, 269, 271, 277, 281, 509, 521, 557, 569, 571, 577, 587, 599, 601, 607, 617, 619, 659, 661, 677, 691, 701, 709, 719, 727, 751
Offset: 1

Views

Author

Jason Bard, Jul 19 2025

Keywords

Crossrefs

Intersection of A038611 and A038612.

Programs

  • Magma
    [p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 5, 6, 7, 8, 9]];
    
  • Maple
    f:= n-> (l-> add([$0..2, $5..9][l[j]+1]*10^(j-1), j=1..nops(l)))(convert(n, base, 8)):
    select(isprime, [seq(f(i), i=0..600)])[];  # Alois P. Heinz, Jul 19 2025
  • Mathematica
    Select[Prime[Range[120]], DigitCount[#, 10, 3] == 0 && DigitCount[#, 10, 4] == 0 &]
  • PARI
    primes_with(, 1, [0, 1, 2, 5, 6, 7, 8, 9]) \\ uses function in A385776
  • Python
    print(list(islice(primes_with("01256789"), 41))) # uses function/imports in A385776
    
Previous Showing 11-13 of 13 results.