cp's OEIS Frontend

A281915 4th power analog of Keith numbers.

%I A281915 #24 Jun 02 2021 22:22:54
%S A281915 1,7,19,20,22,25,28,36,77,107,110,175,789,1528,1932,3778,5200,7043,
%T A281915 8077,38855,41234,44884,49468,204386,763283,9423515,73628992,87146144,
%U A281915 146124072,146293356,326194628,1262293219,1321594778,2767787511,11511913540,12481298961,13639550655
%N A281915 4th power analog of Keith numbers.
%C A281915 Like Keith numbers but starting from n^4 digits to reach n.
%C A281915 Consider the digits of n^4. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some number of iterations reach a sum equal to n.
%e A281915 175^4 = 937890625:
%e A281915 9 + 3 + 7 + 8 + 9 + 0 + 6 + 2 + 5 = 49;
%e A281915 3 + 7 + 8 + 9 + 0 + 6 + 2 + 5 + 49 = 89;
%e A281915 7 + 8 + 9 + 0 + 6 + 2 + 5 + 49 + 89 = 175.
%p A281915 with(numtheory): P:=proc(q, h,w) local a, b, k, t, v; global n; v:=array(1..h);
%p A281915 for n from 1 to q do b:=n^w; a:=[];
%p A281915 for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
%p A281915 for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^w)+1;
%p A281915 t:=nops(a)+1; v[t]:=add(v[k], k=1..b); while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1);
%p A281915 od; if v[t]=n then print(n); fi; od; end: P(10^6,10000,4);
%t A281915 (* function keithQ[ ] is defined in A007629 *)
%t A281915 a281915[n_] := Join[{1, 7}, Select[Range[10, n], keithQ[#, 4]&]]
%t A281915 a281915[10^6] (* _Hartmut F. W. Hoft_, Jun 02 2021 *)
%Y A281915 Cf. A055575, A007629, A246544, A263534.
%Y A281915 Cf. A274769, A274770, A281916, A281917, A281918, A281919, A281920, A281921.
%K A281915 nonn,base
%O A281915 1,2
%A A281915 _Paolo P. Lava_, Feb 02 2017
%E A281915 a(27)-a(28) from _Jinyuan Wang_, Jan 30 2020
%E A281915 Missing a(25) and a(29)-a(37) from _Giovanni Resta_, Jan 31 2020