This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(0) = 4 because by replacing the digit 0, we obtain the 4 primes 2, 3, 5 and 7; a(11) = 7 because by replacing the 1st digit of *1, we obtain the primes 31, 41, 61, 71, and by replacing the 2nd digit of 1* we obtain the primes 13, 17, 19, hence a(11) = 7. a(13) = 8 because 03, 11, 17, 19, 23, 43, 53, 73 and 83 are all primes. a(204) = 0 because it is impossible to find a prime number if we replace the digits 2, 0 or 4.
A209252 := proc(n) local a,dgs,d,r,pd,p ; a := 0 ; dgs := convert(n,base,10) ; for d from 1 to nops(dgs) do for r from 0 to 9 do pd := subsop(d=r,dgs) ; p := add(op(i,pd)*10^(i-1),i=1..nops(pd)) ; if isprime(p) and p <> n then a := a+1 ; end if; end do: end do: a ; end proc: # R. J. Mathar, Jan 18 2013
f[n_] := Block[{c = k = 0, d, p, lmt = 1 + Floor@ Log10@ n}, While[k < lmt, d = 0; While[d < 10, p = Quotient[n, 10^(k+1)]*10^(k+1) + d*10^k + Mod[n, 10^k]; If[p != n && PrimeQ@ p, c++]; d++]; k++]; c]; f[0] = 4; Array[f, 105, 0] (* Robert G. Wilson v, Dec 19 2015 *)
from sympy import isprime def A209252(n): return len([1 for i in range(len(str(n))) for d in '0123456789' if d != str(n)[i] and isprime(int(str(n)[:i]+d+str(n)[i+1:]))]) # Chai Wah Wu, Sep 19 2016
from gmpy2 import digits, is_prime
def a(n):
s, c = list(map(int, digits(n))), 0
if len(s) > 1 and s[-1] not in {1, 3, 7, 9}:
z = int(is_prime(s[-1])) if all(c == 0 for c in s[1:-1]) else 0
return z + sum(1 for e in {1, 3, 7, 9} if is_prime(n + e - s[-1]))
for i in range(len(s)):
b = 10**(len(s)-1-i)
for j in range(10):
if j != s[i]:
t = n + (j-s[i])*b
if is_prime(t):
c += 1
return c
print([a(n) for n in range(100)]) # Michael S. Branicky, Apr 22 2025
NeighborsAndSelf[n_] := Flatten[MapIndexed[Table[ n + (i - #)*10^(#2[[1]] - 1), {i, 0, 9}] &, Reverse[IntegerDigits[n, 10]]]]
PrimeNeighbors[n_] := Complement[Select[NeighborsAndSelf[n],PrimeQ],{n}]
WeaklyTwinPrime[p_] := (Length[#] == 1 && PrimeNeighbors[#[[1]]] == {p}) &[PrimeNeighbors[p]]
For[k = 0, k <= PrimePi[10^10], k++, If[WeaklyTwinPrime[Prime[k]], Print[Prime[k]]]]
The 1-digit optimal prime ladder 3 - 5 is tied for the longest amongst 1-digit primes, so a(1) = 2. The 2-digit optimal prime ladder 97 - 17 - 13 - 53 is tied for the longest amongst 2-digit primes, so a(2) = 4. The 3-digit optimal prime ladder 389 - 383 - 283 - 281 - 251 - 751 - 761 is tied for the longest amongst 3-digit primes, so a(3) = 7. The 4-digit optimal prime ladder 4651 - 4951 - 4931 - 4933 - 4733 - 6733 - 6833 - 6883 - 6983 is tied for the longest amongst 4-digit primes, so a(4) = 9. The 5-digit optimal prime ladder 88259 - 48259 - 45259 - 45959 - 41959 - 41969 - 91969 - 91961 - 99961 - 99761 - 99721 is tied for the longest amongst 5-digit primes, so a(5) = 13. The 6-digit optimal prime ladder 440497 - 410497 - 410491 - 710491 - 710441 - 710443 - 717443 - 917443 - 917843 - 907843 - 905843 - 905833 - 995833 is tied for the longest amongst 6-digit primes, so a(6) = 13. The 7-digit optimal prime ladder 3038459 - 3032459 - 3032453 - 3034453 - 3034457 - 3034657 - 3074657 - 3074557 - 4074557 - 4079557 - 4779557 - 4779547 - 7779547 - 7759547 - 7755547 is tied for the longest amongst 7-digit primes, so a(7) = 15. - _Michael S. Branicky_, May 21 2022
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