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A090422 Primes that cannot be written in binary representation as concatenation of other primes. 5
2, 3, 5, 7, 13, 17, 19, 37, 41, 53, 67, 73, 89, 97, 101, 103, 107, 131, 137, 139, 149, 163, 193, 197, 199, 211, 227, 257, 263, 269, 277, 281, 293, 307, 311, 313, 331, 389, 397, 401, 409, 419, 421, 443, 449, 461, 521, 523, 547, 557, 569, 571, 577, 587, 593 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A090418(a(n)) = 1; subsequence of A090421.
This sequence is indeed infinite, as we need infinitely many terms to cover the primes with arbitrarily large runs of 0's in their base-2 representation. - Jeffrey Shallit, Mar 07 2021
LINKS
PROG
(Haskell)
a090422 n = a090422_list !! (n-1)
a090422_list = filter ((== 1) . a090418 . fromInteger) a000040_list
-- Reinhard Zumkeller, Aug 07 2012
(Python)
from sympy import isprime, primerange
def ok(p):
b = bin(p)[2:]
for i in range(2, len(b)-1):
if isprime(int(b[:i], 2)) and b[i] != '0':
if isprime(int(b[i:], 2)) or not ok(int(b[i:], 2)): return False
return True
def aupto(lim): return [p for p in primerange(2, lim+1) if ok(p)]
print(aupto(593)) # Michael S. Branicky, Mar 07 2021
CROSSREFS
A342244 handles the case where the primes are allowed to have leading zeros.
Sequence in context: A109461 A138539 A337119 * A005109 A247980 A234851
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Nov 30 2003
EXTENSIONS
Based on corrections in A090418, data recomputed by Reinhard Zumkeller, Aug 07 2012
STATUS
approved

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Last modified March 1 15:29 EST 2024. Contains 370440 sequences. (Running on oeis4.)