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A292512
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = my (A=n + sum digits(n), B=n + sum digits(n, 100)); while (1, if (A==B, return (A), A<B, A += sum digits(A), B += sum digits(B, 100))) \\ Rémy Sigrist, Sep 23 2017
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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