A020449 - OEIS

%I #61 Jan 14 2023 08:44:19

%S 11,101,10111,101111,1011001,1100101,10010101,10011101,10100011,

%T 10101101,10110011,10111001,11000111,11100101,11110111,11111101,

%U 100100111,100111001,101001001,101001011,101100011,101101111,101111011,101111111

%N Primes whose greatest digit is 1.

%C Primes which are the sums of distinct powers of 10. - _Amarnath Murthy_, Nov 19 2002

%C Subsequence of A007088. - _Michel Marcus_, Dec 18 2015

%C These numbers are called Anti-Yarborough prime numbers in the Prime Glossary. - _Randy L. Ekl_, Jan 19 2019

%H Jon E. Schoenfield, <a href="/A020449/b020449.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%H C. K. Caldwell, The Prime Glossary, <a href="https://primes.utm.edu/glossary/page.php?sort=YarboroughPrime">Yarborough prime</a>.

%H <a href="/index/Pri#PrimesWithDigits">Index to entries for primes with digits in a given set</a>

%p N:= 10: # to get all entries with <= N digits

%p S:= {}:

%p for d from 1 to N-1 do

%p   S:= S union select(isprime,map(`+`,map(convert,combinat[powerset]({seq(10^i,i=0..d-1)}),`+`),10^d));

%p od:

%p S; # if using Maple 11 or earlier, uncomment the next line

%p # sort(convert(%,list)); # _Robert Israel_, May 04 2015

%t Flatten[Table[Select[FromDigits/@Tuples[{0,1},n],PrimeQ],{n,9}]] (* _Vincenzo Librandi_, Jul 27 2012 *)

%o (Magma) [p: p in PrimesUpTo(101111111) | Set(Intseq(p)) subset [0,1]]; // _Vincenzo Librandi_, Jul 27 2012

%o (PARI) is(n)=isprime(n)&&vecmax(digits(n))==1 \\ _Charles R Greathouse IV_, Jul 01 2013

%o (Python)

%o from sympy import isprime

%o A020449_list = [n for n in (int(format(m,'b')) for m in range(1,2**10)) if isprime(n)] # _Chai Wah Wu_, Dec 17 2015

%Y Cf. A007088, A036952.

%K nonn,base

%O 1,1

%A _David W. Wilson_