cp's OEIS Frontend

A255968 Numbers k such that antisigma(k) contains k as a substring.

%I A255968 #24 Jun 24 2025 10:45:35
%S A255968 24,57,204,411,559,2004,2440,3935,6616,8640,20004,34939,55827,61009,
%T A255968 64599,79747,87113,87269,96513,481557,621265,647532,702893,704682,
%U A255968 797465,2000004,2385120,4066960,4566616,8984375,20000004,54636003,65061605
%N A255968 Numbers k such that antisigma(k) contains k as a substring.
%C A255968 Any number of the form 20...04, with a number of consecutive zeros not equal to 6*k+4 (with k = 0, 1, 2, 3,...), appears to belong to the sequence.
%e A255968 antisigma(24) = (24*25) / 2 - sigma(24) = 300 - 60 = 240 and 24 is a substring;
%e A255968 antisigma(57) = (57*58) / 2 - sigma(57) =  1653 - 80 = 1573 and 57 is a substring.
%p A255968 with(numtheory): P:=proc(q) local a,b,c,d,j,n;
%p A255968 for n from 1 to q do a:=n; b:=n*(n+1)/2-sigma(n); c:=ilog10(n)+1; d:=ilog10(b)+1;
%p A255968 for j from 1 to d-c+1 do if n=(b mod 10^c) then print(n); break; else b:=trunc(b/10);
%p A255968 fi; od; od; print(); end: P(10^9);
%t A255968 Select[Range[800000],SequenceCount[IntegerDigits[(#(#+1))/2-DivisorSigma[1,#]],IntegerDigits[#]]>0&] (* The program generates the first 25 terms of the sequence. *) (* _Harvey P. Dale_, Jun 23 2025 *)
%Y A255968 Cf. A024816.
%K A255968 nonn,base
%O A255968 1,1
%A A255968 _Paolo P. Lava_, Mar 12 2015
%E A255968 a(28)-a(33) from _Robert Israel_, Dec 20 2024