A048853 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).
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, 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, 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
Offset: 1
Examples
Altering the number 13 gives eight primes: 11, 17, 19, 23, 43, 53, 73, 83, so a(13)=8.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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Haskell
import Data.List (inits, tails, nub) a048853 n = (sum $ map (a010051 . read) $ tail $ nub $ concat $ zipWith (\its tls -> map ((\xs ys d -> xs ++ (d:ys)) its tls) "0123456789") (map init $ tail $ inits $ show n) (tail $ tails $ show n)) - a010051 n -- Reinhard Zumkeller, Jul 05 2011 -
Maple
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
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Mathematica
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 *) -
Python
from sympy import isprime def h1(n): # hamming distance 1 neighbors of n, not starting with 0 s = str(n); d = "0123456789"; L = len(s) 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")) def a(n): return sum(1 for k in h1(n) if isprime(k)) print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Jul 31 2022
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