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

1,1

Links

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

Example

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}

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

Prog

(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
(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

Crossrefs

Cf. A000040.

Sequence in context: A244584 A369233 A092531 * A285245 A098528 A242715

Adjacent sequences: A124999 A125000 A125001 * A125003 A125004 A125005

Keyword

nonn,base

Author

Zak Seidov, Jan 08 2007

Extensions

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

Status

approved