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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 Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 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 Cf. A090423, A000040, A004676, A007088. A342244 handles the case where the primes are allowed to have leading zeros. Sequence in context: A109461 A138539 A337119 * A005109 A247980 A234851 Adjacent sequences: A090419 A090420 A090421 * A090423 A090424 A090425 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.)