A125002 Let p = prime(n); a(n) = number of primes q with same number of digits as p that can be obtained from p by changing one digit.

3, 3, 3, 3, 7, 8, 7, 7, 6, 5, 5, 5, 6, 7, 6, 6, 5, 5, 5, 6, 7, 6, 6, 5, 4, 10, 8, 11, 11, 6, 8, 9, 9, 10, 6, 7, 11, 9, 9, 8, 7, 6, 10, 9, 11, 9, 7, 8, 7, 6, 7, 7, 7, 7, 8, 9, 5, 7, 7, 7, 9, 6, 8, 6, 7, 8, 5, 8, 9, 6, 7, 6, 8, 7, 6, 8, 4, 8, 8, 10, 8, 6, 9, 6, 11, 5, 8, 7, 8, 8, 7, 7, 5, 8, 8, 5, 7, 5, 6, 6

Offset: 1

Author

Zak Seidov, Jan 08 2007

Keywords

• nonn
• base

Examples

			The 5th prime 11 leads to 7 other primes: 13,17,19,31,41,61,71, hence a(5)=7.
a(6)=8, p=13, q={11,17,19,23,43,53,73,83}
a(7)=7, p=17, q={11,13,19,37,47,67,97}
a(8)=7, p=19, q={11,13,17,29,59,79,89}
a(9)=6, p=23, q={29,13,43,53,73,83}
a(10)=5, p=29, q={23,19,59,79,89}
		

Links

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

Crossrefs

Cf. A000040.

Programs

Haskell

import Data.List (delete)
a125002 n = sum $ map (a010051' . read) $
                  tail $ concatMap (f pds) [0 .. length pds - 1] where
   pds = show $ a000040 n
   f ws k = [us ++ [y] ++ vs |
            let (us, v:vs) = splitAt k ws, y <- delete v "0123456789"]
-- Reinhard Zumkeller, Jul 06 2014

Maple

A125002 := proc(n) local p,digs,res,r,d; p := ithprime(n) ; digs := convert(p,base,10) ; res := 0 ; for d from 1 to nops(digs) do for r from 0 to 9 do if r <> op(d,digs) and ( d <> nops(digs) or r > 0) then q := p-(op(d,digs)-r)*10^(d-1) ; if isprime(q) then res := res+1 ; fi ; fi ; od ; od ; RETURN(res) ; end ; for n from 1 to 100 do printf("%d,",A125002(n)) ; od ; # R. J. Mathar, Jan 13 2007

Python

from sympy import isprime, sieve
def neighbors(s):
    digs = "0123456789"
    ham1 = (s[:i]+d+s[i+1:] for i in range(len(s)) for d in digs if d!=s[i])
    yield from (h for h in ham1 if h[0] != '0')
def a(n):
    return sum(1 for s in neighbors(str(sieve[n])) if isprime(int(s)))
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, May 09 2022

Extensions

Corrected and extended by Hans Havermann and R. J. Mathar, Jan 08 2007