login
A166744
Unlucky primes: numbers which are members of both A000040 (primes) and A050505 (unlucky).
1
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
1,1
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
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
PROG
(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
CROSSREFS
Cf. A007528, A031157 (lucky primes).
Sequence in context: A009770 A132121 A070957 * A080165 A239712 A224363
KEYWORD
nonn
AUTHOR
Gabriel Finch (salsaman(AT)xs4all.nl), Oct 21 2009
STATUS
approved