A057333 Numbers of n-digit primes that undulate.

4, 20, 74, 347, 1743, 8385, 44355, 229952, 1235489, 6629026, 37152645, 202017712, 1142393492, 6333190658

Offset: 1

Author

Patrick De Geest, Sep 15 2000

Keywords

• nonn
• base
• more

Comments

'Undulate' means that the alternate digits are consistently greater than or less than the digits adjacent to them (e.g., 70769). Smoothly undulating palindromic primes (e.g., 95959) are a subset and included in the count.

References

• C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123-124, 316-317.

Links

• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
• Eric Weisstein's World of Mathematics, Undulating Number.

Crossrefs

Cf. A046075, A033619, A032758, A039944, A016073, A046076, A046077, A057332.

Programs

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):
                yield s+str(t)
    else:
        for s in w:
            for t in range(0,int(s[-1])):
                yield s+str(t)
def A057333(n):
    c = 0
    for d in '123456789':
        x = d
        for i in range(1,n):
            x = f(x,(-1)**i)
        c += sum(1 for p in x if isprime(int(p)))
        if n > 1:
            y = d
            for i in range(1,n):
                y = f(y,(-1)**(i+1))
            c += sum(1 for p in y if isprime(int(p)))
    return c # Chai Wah Wu, Apr 25 2021

Extensions

Offset corrected and a(10)-a(11) from Donovan Johnson, Aug 08 2010

a(12) from Giovanni Resta, Feb 24 2013

a(2) corrected by Chai Wah Wu, Apr 25 2021

a(13)-a(14) from Chai Wah Wu, May 02 2021