cp's OEIS Frontend

A206768 a(n) = smallest number k such that sigma(k-n) = sigma(k) - n, with k > n+1.

%I A206768 #28 Jun 11 2016 03:42:43
%S A206768 3,5,5,7,7,11,81,11,11,13,13,17,4431,17,17,19,19,23,25,23,23,29
%N A206768 a(n) = smallest number k such that sigma(k-n) = sigma(k) - n, with k > n+1.
%C A206768 This sequence begins
%C A206768 3, 5, 5, 7, 7, 11, 81, 11, 11, 13, 13, 17, 4431, 17, 17, 19, 19, 23, 25, 23, 23, 29, ?, 29, ?, 29, 29, 31, 31, 37, ?, 37, 51, 37, 37, 41, 81, 41, 41, 43, 43, 47, ?, 47, 47, 53, ?, 53, 3364, 53, 53, 59, ?, 59, ?, 59, 59, 61, 61, 67, ?, 67, ?, 67, 67, 71, ?, 71, 71, 73, 73, 79, 91, 79, ?, 79, 79, 83, ?, 83, 83, 89, ?, 89, ?, 89, 89, 101, ?, 97, ?, 97, 125, 97, 97, 101, ?, 101, 101, 103, 103, 107... where the other missing terms (designated by "?") are > 10^6, if they exist.
%C A206768 For a given n, n being even, among the integers k satisfying the property sigma(k-n) = sigma(k)-n, we will find prime numbers p, such that p and p-n are primes. This is because in that case sigma(p-n) = (p-n)+1 = (p+1)-n = sigma(p)-n. For instance, when n is even, for n=2 to 14, a(n) is the first term of A006512, A046132, A046117, A092402, A092146, A092216, A098933. If we restrict to composite numbers, then see A084293. - _Michel Marcus_, Feb 16 2013
%C A206768 For the missing terms mentioned in first comment, a(n) is > 10^7. - _Michel Marcus_, Sep 21 2013
%e A206768 a(13) = 4431 because 4431 is the minimum number for which sigma(4431-13) = sigma(4418)= 6771 and sigma(4431) - 13 = 6784 -13 = 6771.
%e A206768 a(19) = 25 because 25 is the minimum number for which sigma(25-19) = sigma(6) = 12 and sigma(25) - 19 = 31 -19 = 12.
%p A206768 A206768:=proc(q)
%p A206768 local k,n;
%p A206768 for n from 1 to q do
%p A206768   for k from n+1 to q do
%p A206768   if sigma(-n+k)=sigma(k)-n then print(k); break; fi;
%p A206768 od; od; end:
%p A206768 A206768(1000000000);
%Y A206768 Cf. A015886.
%K A206768 nonn,more,hard
%O A206768 1,1
%A A206768 _Paolo P. Lava_, Jan 10 2013