A020461 -id:A020461 - cp's OEIS frontend

A138126 Indices among the primes of the primes in A020461.

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

Omar E. Pol, Mar 25 2008

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

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

Cf. A000040, A020461, A054356, A138132.

A199340 Primes having only {0, 3, 4} as digits.

Original entry on oeis.org

3, 43, 433, 443, 3343, 3433, 4003, 30403, 33343, 33403, 34033, 34303, 34403, 40343, 40433, 43003, 43403, 300043, 300343, 304033, 304303, 304433, 330433, 333433, 334043, 334333, 334403, 343303, 343333, 343433, 400033, 403003, 403043, 403433, 430303, 430333

Offset: 1

M. F. Hasler, Nov 05 2011

All terms end in '3'. This could be used to speed up the given program.

A020461 is a subsequence. - Vincenzo Librandi, Jul 23 2015

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries about primes with digits in a given set.

Cf. Primes that contain only the digits (3,4,k): this sequence (k=0), A199341 (k=1), A199342 (k=2), A199345 (k=5), A199346 (k=6), A199347 (k=7), A199348 (k=8), A199349 (k=9).
Cf. A020449 - A020472, A199325 - A199329.
Cf. A058429, A058430.

[p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [3, 4, 0]]; // Vincenzo Librandi, Jul 23 2015

Select[Prime[Range[5 10^4]], Complement[IntegerDigits[#], {3, 4, 0}]=={} &] (* Vincenzo Librandi, Jul 23 2015 *)
Select[FromDigits/@Tuples[{0,3,4},6],PrimeQ] (* Harvey P. Dale, Mar 21 2020 *)
Select[10#+3&/@FromDigits/@Tuples[{0,3,4},5],PrimeQ] (* Harvey P. Dale, May 02 2022 *)

a(n, list=0, L=[0, 3, 4], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal && !isprime(A004086(t)) && next; list && print1(t", "); n--||return(t)))} \\ Syntax updated for current PARI version. - M. F. Hasler, Jul 25 2015

{forprime(p=3,1e6,p%10==3&&!setminus(Set(digits(p)),[3,4])&&print1(p","))} \\ [0] evaluates to false. - M. F. Hasler, Jul 25 2015

A199349 Primes having only {3, 4, 9} as digits.

Original entry on oeis.org

3, 43, 349, 433, 439, 443, 449, 499, 3343, 3433, 3449, 3499, 3943, 4339, 4349, 4493, 4933, 4943, 4993, 4999, 9343, 9349, 9433, 9439, 9949, 33343, 33349, 33493, 34439, 34499, 34939, 34949, 39343, 39439, 39443, 39499, 43399, 43499, 43933, 43943, 44449, 44939, 49333, 49339, 49393, 49433, 49499, 49939, 49943, 49993

Offset: 1

M. F. Hasler, Nov 05 2011

A020461 and A020466 are subsequences. - Vincenzo Librandi, Jul 30 2015

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries about primes with digits in a given set.

Cf. Primes that contain only the digits (3,4,k): A199340 (k=0), A199341 (k=1), A199342 (k=2), A199345 (k=5), A199346 (k=6), A199347 (k=7), A199348 (k=8).

Cf. A020449 - A020472, A199325 - A199329.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [3, 4, 9]]; // Vincenzo Librandi, Jul 30 2015

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {3, 4, 9}]=={} &] (* Vincenzo Librandi, Jul 30 2015 *)
Select[Flatten[Table[FromDigits/@Tuples[{3,4,9},n],{n,5}]],PrimeQ] (* Harvey P. Dale, May 02 2023 *)

a(n, list=0, L=[3,4,9], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vecextract(L,v)*u) || next; reqpal && !isprime(A004086(t)) && next; list && print1(t", "); n--||return(t)))}

A020454 Primes that contain digits 1 and 6 only.

Original entry on oeis.org

11, 61, 661, 6661, 11161, 16111, 16661, 66161, 111611, 161611, 611111, 616111, 1111661, 1611161, 1616161, 1616611, 1661111, 1661161, 1666111, 6111661, 6116111, 6116161, 6161161, 6611611, 6661111, 6661661, 11111161, 11166611, 11616611

Offset: 1

David W. Wilson

Jason Bard, Table of n, a(n) for n = 1..10000 (First 1000 terms from Vincenzo Librandi)

[p: p in PrimesUpTo(11616611) | Set(Intseq(p)) subset [1, 6]]; // Vincenzo Librandi, Jul 27 2012. (see Berselli A020461).

Flatten[Table[Select[FromDigits/@Tuples[{1,6},n],PrimeQ],{n,8}]] (* Vincenzo Librandi, Jul 27 2012 *)
Select[Flatten[Table[10*FromDigits/@Tuples[{1,6},n]+1,{n,7}]],PrimeQ] (* Slightly faster than the above Mathematica program by forcing the last digit to be one. *) (* Harvey P. Dale, May 31 2018 *)

A199341 Primes having only {1, 3, 4} as digits.

Original entry on oeis.org

3, 11, 13, 31, 41, 43, 113, 131, 311, 313, 331, 431, 433, 443, 1433, 3313, 3331, 3343, 3413, 3433, 4111, 4133, 4441, 11113, 11131, 11311, 11411, 11443, 13313, 13331, 13411, 13441, 14143, 14341, 14411, 14431, 31333, 33113, 33311, 33331, 33343, 33413, 34141, 34313

Offset: 1

M. F. Hasler, Nov 05 2011

A020451, A020452 and A020461 are subsequences. - Vincenzo Librandi, Jul 26 2015

Robert Israel, Table of n, a(n) for n = 1..10000
Andrew Granville, Missing digits, and good approximations, arXiv:2308.03126 [math.NT], 2023. See p. 4.

Cf. A020449 - A020472, A199325 - A199329.

Cf. similar sequences listed in A199340.

[p: p in PrimesUpTo(10^5) | Set(Intseq(p)) subset [3, 4, 1]]; // Vincenzo Librandi, Jul 26 2015

Dmax:= 5: # to get all terms < 10^Dmax
Cd:= {1,3,4}:
C:= Cd:
for d from 2 to Dmax do
  Cd:= map(t -> (10*t+1,10*t+3,10*t+4),Cd);
  C:= C union Cd;
od:
sort(convert(select(isprime,C),list)); # Robert Israel, Jul 26 2015

Select[Prime[Range[4 10^3]], Complement[IntegerDigits[#], {3, 4, 1}]=={} &] (* Vincenzo Librandi, Jul 26 2015 *)

a(n, list=0, L=[1, 3, 4], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal & !isprime(A004086(t)) & next; list & print1(t", "); n--||return(t)))}

A199342 Primes having only {2, 3, 4} as digits.

Original entry on oeis.org

2, 3, 23, 43, 223, 233, 433, 443, 2243, 2333, 2423, 3323, 3343, 3433, 4243, 4423, 22343, 22433, 23333, 24223, 24443, 32233, 32323, 32423, 32443, 33223, 33343, 42223, 42323, 42433, 42443, 43223, 222323, 223243, 223423, 224233, 224423, 224443, 232333, 232433, 233323, 233423, 234323, 234343, 242243, 243233, 243343, 243433, 244243, 244333

Offset: 1

M. F. Hasler, Nov 05 2011

A020458 and A020461 are subsequences. - Vincenzo Librandi, Jul 28 2015

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A020449 - A020472, A199325 - A199329, A385768 - A385800.

Cf. similar sequences listed in A199340.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [3, 4, 2]]; // Vincenzo Librandi, Jul 28 2015

Select[Prime[Range[10^5]], Complement[IntegerDigits[#], {3, 4, 2}]=={}&] (* Vincenzo Librandi, Jul 28 2015 *)
Table[Select[FromDigits/@Tuples[{2,3,4},n],PrimeQ],{n,6}]//Flatten (* Harvey P. Dale, Nov 06 2019 *)

a(n, list=0, L=[2, 3, 4], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal & !isprime(A004086(t)) & next; list & print1(t", "); n--||return(t)))}

A199346 Primes having only {3, 4, 6} as digits.

Original entry on oeis.org

3, 43, 433, 443, 463, 643, 3343, 3433, 3463, 3643, 4363, 4463, 4643, 4663, 6343, 33343, 36343, 36433, 36643, 43633, 44633, 46633, 46643, 46663, 63443, 63463, 64333, 64433, 64633, 64663, 66343, 66463, 66643, 333433, 334333, 334363, 334643, 336463, 336643, 343333, 343433, 344363, 346433, 363343, 363463, 364333, 364433, 364643

Offset: 1

M. F. Hasler, Nov 05 2011

All terms end in 3 and have a number of digits '4' that is not divisible by 3.

A020461 is a subsequence. - Vincenzo Librandi, Jul 29 2015

Jason Bard, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A020449 - A020472, A199325 - A199329, A385768 - A385800.

Cf. similar sequences listed in A199340.

[p: p in PrimesUpTo(4*10^5) | Set(Intseq(p)) subset [3, 4, 6]]; // Vincenzo Librandi, Jul 29 2015

Select[Flatten[Table[FromDigits/@(Flatten[{#,3},1]&/@Tuples[{3,4,6},n]),{n,0,5}]],PrimeQ] (* Harvey P. Dale, Jan 01 2013 *)
Select[Prime[Range[10^5]], Complement[IntegerDigits[#], {3, 4, 6}]=={}&] (* Vincenzo Librandi, Jul 28 2015 *)

a(n, list=0, L=[3, 4, 6], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u) || next; reqpal & !isprime(A004086(t)) & next; list & print1(t", "); n--||return(t)))}

A054356 The Five Hysterical Girls Theorem.

Original entry on oeis.org

3343, 33343, 333433, 334333, 333333433343

Offset: 1

Antti Karttunen, May 07 2000

Mentioned in the play "The Five Hysterical Girls Theorem" by Rinne Groff at the Connelly Theater in the East Village (2000). Review: New York Times, Apr 27 2000.

The definition suggests that the sequence contains only five terms, probably randomly selected from A270338. - Arkadiusz Wesolowski, Mar 15 2016

From a posting by Adam Stephanides (adamsteph(AT)earthlink.net) to sci.math, circa May 07 2000.

Alex Kasman, Comments
Bruce Weber, Theater Review

Cf. A020461, A036940, A138132. Subsequence of A270338.

Broken link corrected by R. J. Mathar, Feb 05 2010

A036314 Composite numbers whose prime factors contain no digits other than 3 and 4.

Original entry on oeis.org

9, 27, 81, 129, 243, 387, 729, 1161, 1299, 1329, 1849, 2187, 3483, 3897, 3987, 5547, 6561, 10029, 10299, 10449, 11691, 11961, 16641, 18619, 19049, 19683, 30087, 30897, 31347, 35073, 35883, 49923, 55857, 57147, 59049, 79507, 90261, 92691

Offset: 1

Patrick De Geest, Dec 15 1998

All terms are a product of at least two terms of A020461. - David A. Corneth, Oct 09 2020

David A. Corneth, Table of n, a(n) for n = 1..10000
Index entries for sequences related to prime factors.

Cf. A020461, A036302-A036325.

Sum_{n>=1} 1/a(n) = Product_{p in A020461} (p/(p - 1)) - Sum_{p in A020461} 1/p - 1 = 0.1819438988... . - Amiram Eldar, May 22 2022

A036940 Smallest n-digit prime containing only digits 3 and 4, or 0 if no such prime exists.

Original entry on oeis.org

3, 43, 433, 3343, 33343, 333433, 3333433, 34333333, 333334333, 3333334343, 33333333343, 333333343333, 3333333333433, 33333333433333, 333333333334343, 3333333333333343, 33333333333433433, 333333333333334343

Offset: 1

Patrick De Geest, Jan 04 1999

Jinyuan Wang, Table of n, a(n) for n = 1..500

Cf. A020461, A036229, A036314.

Table[SelectFirst[FromDigits/@Tuples[{3,4},n],PrimeQ],{n,18}] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, May 29 2015 *)

cp's OEIS Frontend

A138126 Indices among the primes of the primes in A020461.

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A199340 Primes having only {0, 3, 4} as digits.

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Magma

Mathematica

PARI

PARI

A199349 Primes having only {3, 4, 9} as digits.

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Magma

Mathematica

PARI

A020454 Primes that contain digits 1 and 6 only.

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Magma

Mathematica

A199341 Primes having only {1, 3, 4} as digits.

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Magma

Maple

Mathematica

PARI

A199342 Primes having only {2, 3, 4} as digits.

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Magma

Mathematica

PARI

A199346 Primes having only {3, 4, 6} as digits.

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Magma

Mathematica

PARI

A054356 The Five Hysterical Girls Theorem.

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