A080608 -id:A080608 - cp's OEIS frontend

A322472 Primes that are not base-9 deletable primes (written in base 10).

13, 17, 37, 73, 89, 97, 109, 113, 127, 131, 139, 149, 151, 157, 197, 227, 251, 257, 271, 277, 293, 307, 311, 313, 337, 359, 379, 397, 409, 419, 421, 433, 439, 457, 463, 487, 499, 503, 521, 523, 541, 569, 577, 587, 599, 601, 613, 617, 619, 631, 653, 661, 683, 733, 739, 743, 757, 761

Offset: 1

Robert Price, Dec 09 2018

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime.
Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.
Complement of all primes and A322471.

Robert Price, Table of n, a(n) for n = 1..889

Cf. A080608, A080603, A096235-A096246, A321657.

b = 9; d = {};
p = Select[Range[2, 10000], PrimeQ[#] &];
For[i = 1, i <= Length[p], i++,
c = IntegerDigits[p[[i]], b];
If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];
For[j = 1, j <= Length[c], j++,
t = Delete[c, j];
If[t[[1]] == 0, Continue[]];
If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]]; Complement[Table[Prime[n], {n, PrimePi[Last[d]]}], d] (* Robert Price, Dec 09 2018 *)

A322476 Primes that are not base-11 deletable primes (written in base 10).

Original entry on oeis.org

11, 17, 19, 53, 67, 89, 97, 103, 107, 109, 127, 131, 137, 139, 157, 163, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 239, 241, 269, 277, 281, 307, 311, 379, 383, 397, 401, 419, 421, 431, 443, 449, 463, 467, 491, 499, 503, 541, 547, 569, 571, 577, 587, 593, 599, 601, 607, 613

Offset: 1

Robert Price, Dec 09 2018

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime.
Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.
Complement of all primes and A322475.

Robert Price, Table of n, a(n) for n = 1..890

Cf. A080608, A080603, A096235-A096246, A321657.

b = 11; d = {};
p = Select[Range[2, 10000], PrimeQ[#] &];
For[i = 1, i <= Length[p], i++,
c = IntegerDigits[p[[i]], b];
If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];
For[j = 1, j <= Length[c], j++,
t = Delete[c, j];
If[t[[1]] == 0, Continue[]];
If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]]; Complement[Table[Prime[n], {n, PrimePi[Last[d]]}], d] (* Robert Price, Dec 09 2018 *)

A322478 Primes that are not base-12 deletable primes (written in base 10).

Original entry on oeis.org

13, 73, 97, 109, 157, 193, 241, 313, 337, 397, 409, 421, 431, 577, 601, 631, 661, 673, 691, 797, 877, 929, 937, 941, 1009, 1019, 1021, 1033, 1063, 1093, 1103, 1117, 1123, 1129, 1151, 1153, 1201, 1249, 1297, 1303, 1307, 1321, 1381, 1429, 1439, 1453, 1489, 1549, 1597, 1609, 1619, 1657, 1693, 1741

Offset: 1

Robert Price, Dec 09 2018

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime.
Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.
Complement of all primes and A322477.

Robert Price, Table of n, a(n) for n = 1..319

Cf. A080608, A080603, A096235-A096246, A321657.

b = 12; d = {};
p = Select[Range[2, 10000], PrimeQ[#] &];
For[i = 1, i <= Length[p], i++,
c = IntegerDigits[p[[i]], b];
If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];
For[j = 1, j <= Length[c], j++,
t = Delete[c, j];
If[t[[1]] == 0, Continue[]];
If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]]; Complement[Table[Prime[n], {n, PrimePi[Last[d]]}], d] (* Robert Price, Dec 09 2018 *)

A096237 Number of n-digit base-4 deletable primes.

Original entry on oeis.org

2, 3, 9, 26, 75, 213, 615, 1853, 5854, 18664, 61248, 205300, 698575, 2409598, 8408050, 29657194

Offset: 1

Michael Kleber, Feb 28 2003

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Cf. A080608, A080603, A096235-A096246.

b = 4; a = {2}; d = {2, 3};
For[n = 2, n <= 8, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 12 2018 *)

from sympy import isprime
from sympy.ntheory.digits import digits
def ok(n, prevset, base=4):
    if not isprime(n): return False
    s = "".join(str(d) for d in digits(n, base)[1:])
    si = (s[:i]+s[i+1:] for i in range(len(s)))
    return any(t[0] != '0' and int(t, base) in prevset for t in si)
def afind(terms):
    alst = [2]
    s, snxt, base = {2, 3}, set(), 4
    print(len(s), end=", ")
    for n in range(2, terms+1):
        for i in range(base**(n-1), base**n):
            if ok(i, s):
                snxt.add(i)
        s, snxt = snxt, set()
        print(len(s), end=", ")
afind(10) # Michael S. Branicky, Jan 17 2022

a(6)-a(15) from Ryan Propper, Jul 19 2005

a(16) from Michael S. Branicky, Jan 17 2022

A096238 Number of n-digit base-5 deletable primes.

Original entry on oeis.org

2, 6, 14, 32, 69, 156, 377, 855, 2072, 5131, 12922, 32619, 83945, 217305, 571560, 1517012, 4056107

Offset: 1

Michael Kleber, Feb 28 2003

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Cf. A080608, A080603, A096235-A096246.

b = 5; a = {2}; d = {2, 3};
For[n = 2, n <= 8, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 12 2018 *)

12 more terms from Ryan Propper, Jul 19 2005

A096239 Number of n-digit base-6 deletable primes.

Original entry on oeis.org

3, 7, 32, 135, 597, 2787, 13374, 66071, 335895, 1743974, 9216391, 49420750, 268312356

Offset: 1

Michael Kleber, Feb 28 2003

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Cf. A080608, A080603, A096235-A096246.

b = 6; a = {3}; d = {2, 3, 5};
For[n = 2, n <= 5, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 12 2018 *)

from sympy import isprime
from sympy.ntheory.digits import digits
def ok(n, prevset, base=6):
    if not isprime(n): return False
    s = "".join(str(d) for d in digits(n, base)[1:])
    si = (s[:i]+s[i+1:] for i in range(len(s)))
    return any(t[0] != '0' and int(t, base) in prevset for t in si)
def afind(terms):
    alst = [3]
    s, snxt, base = {2, 3, 5}, set(), 6
    print(len(s), end=", ")
    for n in range(2, terms+1):
        for i in range(base**(n-1), base**n):
            if ok(i, s):
                snxt.add(i)
        s, snxt = snxt, set()
        print(len(s), end=", ")
afind(8) # Michael S. Branicky, Jan 17 2022

a(6)-a(11) from Ryan Propper, Jul 19 2005

a(12)-a(13) from Michael S. Branicky, Jan 17 2022

A096240 Number of n-digit base-7 deletable primes.

Original entry on oeis.org

3, 7, 21, 59, 184, 534, 1620, 4889, 15607, 50138, 165569, 551580, 1860565, 6345080

Offset: 1

Michael Kleber, Feb 28 2003

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Cf. A080608, A080603, A096235-A096246.

b = 7; a = {3}; d = {2, 3, 5};
For[n = 2, n <= 7, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 12 2018 *)

9 more terms from Ryan Propper, Jul 19 2005

A096241 Number of n-digit base-8 deletable primes.

Original entry on oeis.org

4, 14, 50, 238, 1123, 5792, 30598, 166056, 927639, 5308458, 30984757

Offset: 1

Michael Kleber, Feb 28 2003

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Cf. A080608, A080603, A096235-A096246, A322443.

b = 8; a = {4}; d = {2, 3, 5, 7};
For[n = 2, n <= 5, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 13 2018 *)

from sympy import isprime
def ok(n, prevset, base=8):
    if not isprime(n): return False
    s = oct(n)[2:]
    si = (s[:i]+s[i+1:] for i in range(len(s)))
    return any(t[0] != '0' and int(t, base) in prevset for t in si)
def afind(terms):
    s, snxt = {2, 3, 5, 7}, set()
    print(len(s), end=", ")
    for n in range(2, terms+1):
        for i in range(8**(n-1), 8**n):
            if ok(i, s):
                snxt.add(i)
        s, snxt = snxt, set()
        print(len(s), end=", ")
afind(7) # Michael S. Branicky, Jan 14 2022

a(6)-a(10) from Ryan Propper, Jul 19 2005

a(11) from D. S. McNeil, Dec 08 2009

A096242 Number of n-digit base-9 deletable primes.

Original entry on oeis.org

4, 14, 58, 221, 911, 3638, 14687, 61435, 262189, 1140171

Offset: 1

Michael Kleber, Feb 28 2003

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Cf. A080608, A080603, A096235-A096246.

b = 9; a = {4}; d = {2, 3, 5, 7};
For[n = 2, n <= 5, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 13 2018 *)

5 more terms from Ryan Propper, Jul 19 2005

A096244 Number of n-digit base-11 deletable primes.

Original entry on oeis.org

4, 16, 73, 288, 1117, 4472, 18120, 74643, 315174, 1348936

Offset: 1

Michael Kleber, Feb 28 2003

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. "Digit" means digit in base b.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Cf. A080608, A080603, A096235-A096246.

b = 11; a = {4}; d = {2, 3, 5, 7};
For[n = 2, n <= 5, n++,
  p = Select[Range[b^(n - 1), b^n - 1], PrimeQ[#] &];
  ct = 0;
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], b];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; ct++;
     Break[]]]];
  AppendTo[a, ct]];
a (* Robert Price, Nov 13 2018 *)

5 more terms from Ryan Propper, Jul 19 2005

cp's OEIS Frontend

A322472 Primes that are not base-9 deletable primes (written in base 10).

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A322476 Primes that are not base-11 deletable primes (written in base 10).

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A322478 Primes that are not base-12 deletable primes (written in base 10).

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A096237 Number of n-digit base-4 deletable primes.

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A096238 Number of n-digit base-5 deletable primes.

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A096239 Number of n-digit base-6 deletable primes.

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A096240 Number of n-digit base-7 deletable primes.

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A096241 Number of n-digit base-8 deletable primes.

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Mathematica

Python

Extensions

A096242 Number of n-digit base-9 deletable primes.

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Author

Keywords