A020449 Primes whose greatest digit is 1.

11, 101, 10111, 101111, 1011001, 1100101, 10010101, 10011101, 10100011, 10101101, 10110011, 10111001, 11000111, 11100101, 11110111, 11111101, 100100111, 100111001, 101001001, 101001011, 101100011, 101101111, 101111011, 101111111

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Comments

Primes which are the sums of distinct powers of 10. - Amarnath Murthy, Nov 19 2002

Subsequence of A007088. - Michel Marcus, Dec 18 2015

These numbers are called Anti-Yarborough prime numbers in the Prime Glossary. - Randy L. Ekl, Jan 19 2019

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
• C. K. Caldwell, The Prime Glossary, Yarborough prime.
• FactorDB, Concatenation of first 35 terms is prime
• Index to entries for primes with digits in a given set

Crossrefs

Subsequence of A036953.

Cf. A007088, A036952.

Programs

Magma

[p: p in PrimesUpTo(101111111) | Set(Intseq(p)) subset [0,1]]; // Vincenzo Librandi, Jul 27 2012

Maple

N:= 10: # to get all entries with <= N digits
S:= {}:
for d from 1 to N-1 do
  S:= S union select(isprime,map(`+`,map(convert,combinat[powerset]({seq(10^i,i=0..d-1)}),`+`),10^d));
od:
S; # if using Maple 11 or earlier, uncomment the next line
# sort(convert(%,list)); # Robert Israel, May 04 2015

Mathematica

Select[FromDigits/@Tuples[{0,1},16],PrimeQ] (* Hans Havermann, May 12 2025 *)

PARI

is(n)=isprime(n)&&vecmax(digits(n))==1 \\ Charles R Greathouse IV, Jul 01 2013

Python

from sympy import isprime
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