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A273663 Least monotonic left inverse for A273670: a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1). 16
0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 18, 18, 19, 20, 21, 21, 22, 22, 23, 24, 25, 25, 26, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 40, 41, 42, 43, 43, 44, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 53, 54, 54, 55, 56, 57, 57, 58, 58, 59, 60, 61, 61 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10080

FORMULA

a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).

Other identities.

For all n >= 0, a(A273670(n)) = n.

PROG

(Scheme, with memoization-macro definec)

(definec (A273663 n) (if (= 1 n) 0 (+ (A257680 (A225901 n)) (A273663 (- n 1)))))

(Python)

from sympy import factorial as f

def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p

def a225901(n):

    s=0

    k=2

    while n:

        d=n%k

        n=n//k

        if d: s=s+(k - d)*f(k - 1)

        k+=1

    return s

def a257680(n): return 1 if '1' in str(a007623(n)) else 0

def a(n): return 0 if n==1 else a257680(a225901(n)) + a(n - 1)

l=[0, 0]

for n in range(2, 101): l.append(a257680(a225901(n)) + l[n - 1])

print(l[1:]) # Indranil Ghosh, Jun 24 2017

CROSSREFS

Left inverse of A273670.

Cf. A225901, A257680.

Cf. also A273662.

Sequence in context: A014245 A096386 A257063 * A135671 A079420 A076895

Adjacent sequences:  A273660 A273661 A273662 * A273664 A273665 A273666

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 30 2016

STATUS

approved

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Last modified July 29 05:50 EDT 2021. Contains 346340 sequences. (Running on oeis4.)