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

1,1

Comments

a(A192545(n)) = 0. - Reinhard Zumkeller, Jul 05 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

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

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A050652-A050673.

Cf. A010051, A158124.

Sequence in context: A188885 A362330 A129344 * A303701 A179845 A180217

Adjacent sequences: A048850 A048851 A048852 * A048854 A048855 A048856

Keyword

base,nonn,easy,nice

Author

G. L. Honaker, Jr. and Patrick De Geest

Status

approved