A048853 - OEIS

%I #26 Jul 31 2022 15:57:07

%S 4,3,3,4,3,4,3,4,4,4,7,4,8,4,4,4,7,4,7,2,7,2,6,2,2,2,7,2,5,2,5,2,8,2,

%T 2,2,5,2,7,3,6,3,7,3,3,3,6,3,8,2,7,2,6,2,2,2,7,2,5,2,5,2,8,2,2,2,5,2,

%U 7,3,6,3,7,3,3,3,8,3,6,2,7,2,6,2,2,2,7,2,5,1,6,1,7,1,1,1,4,1,6,4,10,4,8,4,4

%N Number of primes (different from n) that can be produced by altering one digit of decimal expansion of n (without changing the number of digits).

%C a(A192545(n)) = 0. - _Reinhard Zumkeller_, Jul 05 2011

%H Reinhard Zumkeller, <a href="/A048853/b048853.txt">Table of n, a(n) for n = 1..10000</a>

%e Altering the number 13 gives eight primes: 11, 17, 19, 23, 43, 53, 73, 83, so a(13)=8.

%p A048853 := proc(n::integer) local resul,ddigs,d,c,tmp ; resul := 0 ; ddigs := convert(n,base,10) ; for d from 1 to nops(ddigs) do for c from 0 to 9 do if c = 0 and d = nops(ddigs) then continue ; else if c <> op(d,ddigs) then tmp := [op(1..d-1,ddigs),c,op(d+1..nops(ddigs),ddigs)] ; tst := sum(op(i,tmp)*10^(i-1),i=1..nops(tmp)) ; if isprime(tst) then resul := resul+1 ; fi ; fi ; fi ; od : od ; RETURN(resul) ; end: for n from 1 to 90 do printf("%d,",A048853(n)) ; od ; # _R. J. Mathar_, Apr 25 2006

%t a[n_] := Module[{idn = IntegerDigits[n], id, np = 0}, Do[id = idn; If[ id[[j]] != k, id[[j]] = k; If[ id[[1]] != 0 && PrimeQ[ FromDigits[id]], np = np + 1]], {j, 1, Length[idn]}, {k, 0, 9}]; np]; Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Dec 01 2011 *)

%o (Haskell)

%o import Data.List (inits, tails, nub)

%o a048853 n = (sum $ map (a010051 . read) $ tail $ nub $ concat $ zipWith

%o   (\its tls -> map ((\xs ys d -> xs ++ (d:ys)) its tls) "0123456789")

%o     (map init $ tail $ inits $ show n) (tail $ tails $ show n)) - a010051 n

%o -- _Reinhard Zumkeller_, Jul 05 2011

%o (Python)

%o from sympy import isprime

%o def h1(n): # hamming distance 1 neighbors of n, not starting with 0

%o     s = str(n); d = "0123456789"; L = len(s)

%o     yield from (int(s[:i]+c+s[i+1:]) for c in d for i in range(L) if c!=s[i] and not (i==0 and c=="0"))

%o def a(n): return sum(1 for k in h1(n) if isprime(k))

%o print([a(n) for n in range(1, 106)]) # _Michael S. Branicky_, Jul 31 2022

%Y Cf. A050652-A050673.

%Y Cf. A010051, A158124.

%K base,nonn,easy,nice

%O 1,1

%A _G. L. Honaker, Jr._ and _Patrick De Geest_