A057333 Numbers of n-digit primes that undulate.

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

Offset

1,1

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

Table of n, a(n) for n=1..14.

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Eric Weisstein's World of Mathematics, Undulating Number.

Prog

(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

Crossrefs

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

Sequence in context: A061981 A054611 A329174 * A196432 A302815 A196508

Adjacent sequences: A057330 A057331 A057332 * A057334 A057335 A057336

Keyword

nonn,base,more

Author

Patrick De Geest, Sep 15 2000

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

Status

approved