A343590 Undulating alternating primes.
2, 3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 103, 107, 109, 163, 181, 307, 383, 503, 509, 523, 547, 563, 587, 701, 709, 727, 769, 787, 907, 929, 947, 967, 2141, 2143, 2161, 2309, 2503, 2549, 2707, 2729, 2749, 2767, 2903, 2909, 2927, 2969, 4363, 4507, 4523, 4547, 4549, 4703
Offset: 1
Examples
2143 is a term as it is prime, digits 2, 1, 4 and 3 have even and odd parity alternately, and also alternately fall and rise.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
q[n_] := PrimeQ[n] && AllTrue[Differences[Sign @ Differences[(d = IntegerDigits[n])]], # != 0 &] && AllTrue[Differences @ Mod[d, 2], # != 0 &]; Select[Range[5000], q] (* Amiram Eldar, Apr 21 2021 *)
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Python
from sympy import sieve def sign(n): return (n > 0) - (n < 0) def ok(p): if p < 10: return True s = str(p) t = set(sign(int(s[i])%2-int(s[i-1])%2)*(-1)**i for i in range(1, len(s))) t2 = set(sign(int(s[i])-int(s[i-1]))*(-1)**i for i in range(1, len(s))) return (t == {1} or t == {-1}) and (t2 == {1} or t2 == {-1}) def aupto(limit): return [p for p in sieve.primerange(1, limit+1) if ok(p)] print(aupto(4703)) # Michael S. Branicky, Apr 21 2021 -
Python
from sympy import isprime def f(w,dir): if dir == 1: for s in w: for t in range(int(s[-1])+1,10,2): yield s+str(t) else: for s in w: for t in range(1-int(s[-1])%2,int(s[-1]),2): yield s+str(t) A343590_list = [] for l in range(5): for d in '123456789': x = d for i in range(1,l+1): x = f(x,(-1)**i) A343590_list.extend([int(p) for p in x if isprime(int(p))]) if l > 0: y = d for i in range(1,l+1): y = f(y,(-1)**(i+1)) A343590_list.extend([int(p) for p in y if isprime(int(p))]) # Chai Wah Wu, Apr 25 2021
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