A352346 Common terms between A061078 and A061077.

26, 52, 148, 280, 320, 454, 1150, 1480, 8000, 41650, 80300, 165656, 166088, 614900, 2353700, 2859460, 28233200, 66130400, 68941640, 85717240, 107300320, 131507080, 155478800, 207666520, 1426680920, 1824596800, 2468014900, 2475648820, 5342351060, 5355218900, 5857281500, 8550475900, 36025361120

Offset: 1

Author

Luca Onnis, Mar 12 2022

Keywords

• nonn
• base

Comments

Smarandache's conjecture: there are infinitely many terms.

This is a subsequence of A061076.

Examples

			26 is a term of this sequence, in fact:
26 = 1+3+5+7+9+1*1 (A061077(6)=26);
26 = 2+4+6+8+1*0+1*2+1*4 (A061078(7)=26).
		

References

• A. Murthy, Smarandache friendly numbers and a few more sequences, Smarandache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001. Page 267

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..205

Crossrefs

Cf. A061076, A061077, A061078.

Programs

Mathematica

Intersection[Accumulate[Times @@@ IntegerDigits[Range[2, 10000000, 2]]],
Accumulate[Times @@@ IntegerDigits[Range[1, 10000000, 2]]]]

Python

from math import prod
from itertools import islice
def A352346_gen(): # generator of terms
    n1, m1, n2, m2 = 1, 1, 2, 2
    while True:
        if m1 == m2:
            yield m1
        k = 0
        while k == 0:
            n1 += 2
            m1 += (k := prod(int(d) for d in str(n1)))
        while m2 < m1:
            n2 += 2
            m2 += prod(int(d) for d in str(n2))
A352346_list = list(islice(A352346_gen(),20)) # Chai Wah Wu, Mar 21 2022