A166744 Unlucky primes: numbers which are members of both A000040 (primes) and A050505 (unlucky).

2, 5, 11, 17, 19, 23, 29, 41, 47, 53, 59, 61, 71, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 157, 167, 173, 179, 181, 191, 197, 199, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 293, 311, 313, 317, 337, 347, 353, 359, 373, 379, 383, 389

Offset: 1

Author

Gabriel Finch (salsaman(AT)xs4all.nl), Oct 21 2009

Keywords

• nonn

Comments

There are infinitely many unlucky prime numbers, in particular all those of the form 6n - 1, eliminated in the second step of Ulam's procedure for lucky numbers. - Davide Rotondo, Aug 31 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007528, A031157 (lucky primes).

Programs

Maple

L:= [seq(2*i+1, i=0..10^3)]:
for n from 2 while n < nops(L) do
  r:= L[n];
  L:= subsop(seq(r*i=NULL, i=1..nops(L)/r), L);
od:
U:= {2, seq(i,i=3..2*10^3+1,2)} minus convert(L,set):
sort(convert(select(isprime,U),list)); # Robert Israel, Jul 26 2019

SageMath

# Copy from  A000959 - (Robert FERREOL, Nov 19 2014)
def lucky(n):
  L=list(range(1, n+1, 2)); j=1
  while L[j] <= len(L)-1:
    L=[L[i] for i in range(len(L)) if (i+1)%L[j]!=0]
    j+=1
  return(L)
[ p for p in prime_range(1000) if p not in lucky(1000) ] # Hauke Löffler, Jul 26 2019