cp's OEIS Frontend

A258413 Numbers m such that antisigma(m) contains sigma(m) as a substring.

%I A258413 #27 Apr 28 2022 13:29:59
%S A258413 34,79,479,1529,2879,4895,8873,14243,26879,62498,79999,295285,559571,
%T A258413 589219,644735,799999,2012897,2181600,2233033,2395488,6399839,7453541,
%U A258413 7922023,8598719,22928034,26861727,37894930,55056372,63652895,76820471,144726608,174044214
%N A258413 Numbers m such that antisigma(m) contains sigma(m) as a substring.
%C A258413 Prime numbers in the sequence: 79, 479, 2879, 14243, 26879, 79999, 559571, 589219, ...
%C A258413 The primes of the form 8*10^k-1, for k>0, like 79 or 79999, are terms. See A056721. - _Giovanni Resta_, Jun 08 2015
%H A258413 Giovanni Resta, <a href="/A258413/b258413.txt">Table of n, a(n) for n = 1..55</a> (terms < 6*10^10)
%e A258413 sigma(34) = 54 and antisigma(34) = 34*35/2 - 54 = 541, which contains 54 as a substring;
%e A258413 sigma(79) = 80 and antisigma(79) = 79*80/2 - 80 = 3080, which contains 80 as a substring;
%e A258413 sigma(479) = 480 and antisigma(479) = 479*480/2 - 480 = 114480, which contains 480 as a substring.
%p A258413 with(numtheory): P:=proc(q) local a,b,c,d,j,k,n;
%p A258413 for n from 1 to q do a:=sigma(n); c:=ilog10(a)+1; b:=n*(n+1)/2-sigma(n); d:=ilog10(b)+1; for k from 0 to d-c do j:=trunc(b/10^k);
%p A258413 if a=j-trunc(j/10^c)*10^c then print(n); break; fi; od; od; end: P(10^9);
%t A258413 fQ[n_]:=StringMatchQ[ToString[n*(n+1)/2-DivisorSigma[1,n]],___~~ToString[DivisorSigma[1,n]]~~___];Select[Range[10^5],fQ[#]&] (* _Ivan N. Ianakiev_, Jun 18 2015 *)
%t A258413 fQ[n_]:=StringContainsQ[ToString[n*(n+1)/2-DivisorSigma[1,n]],ToString[DivisorSigma[1,n]]];Select[Range[10^5],fQ[#]&] (* much faster *) (* _Ivan N. Ianakiev_, Apr 02 2022 *)
%Y A258413 Cf. A000203, A024816, A255968, A056721.
%K A258413 nonn,base
%O A258413 1,1
%A A258413 _Paolo P. Lava_, May 29 2015
%E A258413 a(16)-a(32) from _Giovanni Resta_, Jun 08 2015