A319744 Partial sums of bouncy numbers (A152054).

101, 203, 306, 410, 515, 621, 728, 836, 945, 1065, 1186, 1316, 1447, 1579, 1719, 1860, 2002, 2145, 2295, 2446, 2598, 2751, 2905, 3065, 3226, 3388, 3551, 3715, 3880, 4050, 4221, 4393, 4566, 4740, 4915, 5091, 5271, 5452, 5634, 5817, 6001, 6186, 6372, 6559, 6749, 6940, 7132, 7325, 7519

Offset: 1

Author

David F. Marrs, Oct 21 2018

Keywords

• nonn
• base

Examples

			a(1) = 101.
a(2) = 101 + 102 = 203.
a(10) = 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 120 = 1065.
		

Links

• David F. Marrs, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A152054 (bouncy numbers).

Programs

Python

for n in range(50):
  a = n
  b = 0
  c = 0
  while a:
    if ''.join(sorted(str(b))) != str(b) and ''.join(sorted(str(b)))[::-1] != str(b): c += b; a -= 1
    b += 1
  print(c)

Python

from itertools import count, islice
def A319744_gen(): # generator of terms
    c = 0
    for n in count(101):
        l = len(s:=tuple(int(d) for d in str(n)))
        for i in range(1,l-1):
            if (s[i-1]-s[i])*(s[i]-s[i+1]) < 0:
                c += n
                yield c
                break
A319744_list = list(islice(A319744_gen(),30)) # Chai Wah Wu, Jul 28 2023