# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a292512 Showing 1-1 of 1 %I A292512 #19 Sep 23 2017 19:22:41 %S A292512 2,4,6,8,10,12,14,16,18,221,341,24,109,218,30,1171,173,36,406,80,84, %T A292512 88,851,96,163,104,54,218,346,120,628,1171,231,173,181,72,197,406,213, %U A292512 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 %N 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. %C A292512 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. %C A292512 The common numbers for the first ten primes are: %C A292512 2 -> 4, 8, 16, 1027975, ... %C A292512 3 -> 24, 96, 60342, ... %C A292512 5 -> 10, 469534, ... %C A292512 7 -> 14, 131558, ... %C A292512 11 -> 923428, ... %C A292512 13 -> 668495, ... %C A292512 17 -> 81820, ... %C A292512 19 -> 2061797, ... %C A292512 23 -> 2227118, ... %C A292512 29 -> 12278, ... %H A292512 Rémy Sigrist, Table of n, a(n) for n = 1..10000 %e A292512 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, ... %e A292512 Sequence B: 10, 20, 40, 80, 160, 221, ... %e A292512 -> 221 is the first common number > 10, so a(n)=221. %t A292512 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 *) %o A292512 (PARI) a(n) = my (A=n + sum digits(n), B=n + sum digits(n,100)); while (1, if (A==B, return (A), A