This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
232564 is an SPN but is not in this sequence since it can be obtained from the SPN 32564 by prefixing the digit 2.
232564 is an SPN but is not primitive since it can be obtained from the SPN 32564 by prefixing the digit 2.
In 3648169, for 3 we can see 9, for 6 we can see 36, for 4 we can see 16, for 8 we can see 64, for 1 we can see 1 and for 9 we can see 81.
fQ[n_] := (id = IntegerDigits@ n; Union[id][[1]] != 0 && Sort[ StringPosition[ ToString[n], ToString[#]] & /@ Evaluate[ id^2]][[1]] != {}); k = 0; lst = {}; While[k < 2*10^7, If[fQ@k, AppendTo[lst, k]; Print@ k]; k++] (* Robert G. Wilson v, Jan 06 2012 *)
sq = {d:str(int(d)**2) for d in "123456789"}
def ok(n): return "0" not in (s:=str(n)) and all(sq[d] in s for d in set(s))
print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, May 05 2023
In the first number, for 2 we can see 4, for 5 we can see 25, for 3 we can see 9, for 6 we can see 36, for 4 we can see 16, for 9 we can see 81, for 8 we can see 64, for 1 we can see 1 and for 7 we can see 49.
24 is a self-factorial number because we can see both 2! = 2 and 4! = 24 in the decimal expansion 24.
import Data.List (nub, sort, isInfixOf)
a134948 n = a134948_list !! (n-1)
a134948_list = filter h [0..] where
h x = all (`isInfixOf` xs)
(map (fss !!) $ map (read . return) $ sort $ nub xs)
where xs = show x
fss = map show $ take 10 a000142_list
-- Reinhard Zumkeller, Sep 26 2014
isA134948 := proc(n) local nbase10,dgs,d,dfac ; nbase10 := convert(n,base,10) ; dgs := convert(nbase10,set) ; for d in dgs do dfac := convert(d!,base,10) ; if verify(dfac,nbase10,'sublist') = false then RETURN(false) ; fi ; od: RETURN(true) ; end: for n from 1 to 10000 do if isA134948(n) then printf("%d ",n) ; fi ; od: # R. J. Mathar, Feb 05 2008
filter:= proc (n) local L, LP; L := convert(n, base, 10); if has(L, 0) then return false end if; if has(L, 1) and not has(L, 2) then return false end if; if has(L, 2) and not has(L, 3) then return false end if; if has(L, 3) and not has(L, 5) then return false end if; if has(L, 4) and not has(L, 7) then return false end if; LP := [seq([L[i], L[i+1]], i = 1 .. nops(L)-1)]; if has(L, 5) and not member([1, 1], LP) then return false end if; if has(L, 6) and not member([3, 1], LP) then return false end if; if has(L, 7) and not member([7, 1], LP) then return false end if; if has(L, 8) and not member([9, 1], LP) then return false end if; if has(L, 9) and not member([3, 2], LP) then return false end if; true end proc: select(filter, [$1..1.5*10^5]);
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