A292512 Sequence A: Start with n, add the sum of digits of n (A062028) and repeat. Sequence B: Start with n, add the sum of base-100 digits of n and repeat. a(n) is the smallest common number > n.

2, 4, 6, 8, 10, 12, 14, 16, 18, 221, 341, 24, 109, 218, 30, 1171, 173, 36, 406, 80, 84, 88, 851, 96, 163, 104, 54, 218, 346, 120, 628, 1171, 231, 173, 181, 72, 197, 406, 213, 538, 260, 237, 1003, 1705, 90, 184, 719, 1041, 1015, 365, 111, 320, 127, 117, 418, 488, 114, 1487, 137, 120, 122, 199, 126, 1171, 298, 231, 134, 677

Offset: 1

Author

Peter Weiss, Sep 18 2017

Keywords

• nonn
• base

Comments

If you start with n=1 and take a third sequence C (n + sum of base-1000 digits of n), the first common numbers of the three sequences are 2, 4, 8, 16 and 1027975.

The common numbers for the first ten primes are:

2 -> 4, 8, 16, 1027975, ...

3 -> 24, 96, 60342, ...

5 -> 10, 469534, ...

7 -> 14, 131558, ...

11 -> 923428, ...

13 -> 668495, ...

17 -> 81820, ...

19 -> 2061797, ...

23 -> 2227118, ...

29 -> 12278, ...

Examples

			n=10: Sequence A: 10, 11, 13, 17, 25, 32, 37, 47, 58, 71, 79, 95, 109, 119, 130, 134, 142, 149, 163, 173, 184, 197, 214, 221, ...
Sequence B: 10, 20, 40, 80, 160, 221, ...
-> 221 is the first common number > 10, so a(n)=221.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A286660, A062028, A007618, A006507, A016096.

Programs

Mathematica

With[{m = 10^3}, Table[With[{A = Rest@ NestList[# + Total@ IntegerDigits@ # &, n, m]}, NestWhile[# + Total@ IntegerDigits[#, 100] &, n, FreeQ[A, #] &, 1, m]], {n, 68}]] (* Michael De Vlieger, Sep 23 2017 *)

PARI

a(n) = my (A=n + sumdigits(n), B=n + sumdigits(n,100)); while (1, if (A==B, return (A), ARémy Sigrist, Sep 23 2017