A096235 -id:A096235 - cp's OEIS frontend

A321910 Base-7 deletable primes (written in base 10).

2, 3, 5, 17, 19, 23, 31, 37, 41, 47, 101, 103, 131, 137, 139, 149, 163, 167, 191, 199, 223, 227, 233, 241, 251, 263, 293, 311, 313, 317, 331, 691, 709, 719, 727, 733, 787, 823, 853, 877, 887, 919, 929, 937, 977, 983, 997, 1013, 1019, 1021, 1031, 1049, 1129, 1171, 1367, 1399, 1409, 1511

Offset: 1

Robert Price, Nov 29 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.

Robert Price, Table of n, a(n) for n = 1..808

Cf. A080608, A080603, A096235-A096246.

b = 7; 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[]]]];
d (* Robert Price, Dec 06 2018 *)

A322173 Base-6 deletable primes (written in base 10).

Original entry on oeis.org

2, 3, 5, 11, 13, 17, 19, 23, 29, 31, 41, 47, 53, 59, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 283, 293, 311, 313, 317, 347, 353, 359, 373, 379, 383, 389, 397

Offset: 1

Robert Price, Nov 29 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.

Robert Price, Table of n, a(n) for n = 1..3561

Cf. A080608, A080603, A096235-A096246.

b = 6; 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[]]]];
d (* Robert Price, Dec 06 2018 *)

A322471 Base-9 deletable primes (written in base 10).

Original entry on oeis.org

2, 3, 5, 7, 11, 19, 23, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 79, 83, 101, 103, 107, 137, 163, 167, 173, 179, 181, 191, 193, 199, 211, 223, 229, 233, 239, 241, 263, 269, 281, 283, 317, 331, 347, 349, 353, 367, 373, 383, 389, 401, 431, 443, 449, 461, 467, 479, 491, 509, 547, 557, 563

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.

Robert Price, Table of n, a(n) for n = 1..327

Cf. A080608, A080603, A096235-A096246.

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[]]]];
d (* Robert Price, Dec 09 2018 *)

A322474 Primes that are not base-10 deletable primes (written in base 10).

Original entry on oeis.org

11, 19, 41, 61, 89, 101, 109, 149, 151, 181, 191, 199, 211, 227, 241, 251, 257, 277, 281, 349, 389, 401, 409, 419, 421, 449, 461, 491, 499, 521, 541, 557, 577, 587, 601, 619, 641, 661, 691, 727, 757, 787, 809, 811, 821, 827, 857, 877, 881, 887, 911, 919, 941, 991, 1009, 1019, 1021, 1049, 1051, 1061

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. Thus 2003 is in this sequence but not in A081027.
Complement of all nonprimes and A305352.

Robert Price, Table of n, a(n) for n = 1..530

Cf. A080608, A080603, A096235-A096246, A321657, A305352, A081027.

b = 10; 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 *)

A322475 Base-11 deletable primes (written in base 10).

Original entry on oeis.org

2, 3, 5, 7, 13, 23, 29, 31, 37, 41, 43, 47, 59, 61, 71, 73, 79, 83, 101, 113, 149, 151, 167, 211, 233, 251, 257, 263, 271, 283, 293, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 389, 409, 433, 439, 457, 461, 479, 487, 509, 521, 523, 557, 563, 631, 653, 659, 673, 677, 719, 733, 739

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.

Robert Price, Table of n, a(n) for n = 1..304

Cf. A080608, A080603, A096235-A096246.

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[]]]];
d (* Robert Price, Dec 09 2018 *)

A322477 Base-12 deletable primes (written in base 10).

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 79, 83, 89, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 317, 331, 347, 349, 353, 359, 367, 373, 379

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.

Robert Price, Table of n, a(n) for n = 1..910

Cf. A080608, A080603, A096235-A096246.

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[]]]];
d (* Robert Price, Dec 09 2018 *)

A096245 Number of n-digit base-12 deletable primes.

Original entry on oeis.org

5, 25, 186, 1398, 11500, 99074, 893062, 8352961, 80564801

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 0's in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Cf. A080608, A080603, A096235-A096246.

b = 12; a = {5}; d = {2, 3, 5, 7, 11};
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
from sympy.ntheory.digits import digits
def strmap(d):
    return str(d) if d < 10 else "ABCDEFGHIJKLMNOPQRSTUVWXYZ"[d-10]
def ok(n, prevset, base=12): # works for bases 2-36
    if not isprime(n): return False
    s = "".join(strmap(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, base=12): # works for bases 3-36
    s = set([p for p in range(1, base) if isprime(p)])
    alst, snxt = [len(s)], set()
    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(6) # Michael S. Branicky, Jan 17 2022

a(6)-a(8) from Ryan Propper, Jul 19 2005
Edited by Charles R Greathouse IV, Aug 03 2010
a(9) from Michael S. Branicky, Jan 17 2022

A320587 Primes that are not Base-3 deletable primes (written in base 10).

Original entry on oeis.org

3, 13, 31, 37, 41, 43, 67, 79, 97, 103, 109, 113, 127, 131, 139, 149, 151, 157, 163, 193, 199, 211, 227, 229, 239, 241, 257, 271, 277, 281, 283, 293, 307, 311, 313, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 433, 439, 443

Offset: 1

Robert Price, Nov 14 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 A319596.

Robert Price, Table of n, a(n) for n = 1..906

Cf. A080608, A080603, A096235-A096246.

b = 3; 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 06 2018 *)

Added the term 3. As pointed out by Kevin Ryde, there is no need to "seed" the list using base-2 assumptions. - Robert Price, Dec 06 2018

A321596 Primes that are not base-2 deletable primes (written in base 10).

Original entry on oeis.org

17, 31, 41, 67, 71, 89, 97, 103, 113, 127, 131, 139, 181, 191, 193, 199, 223, 227, 233, 239, 241, 251, 257, 263, 269, 271, 283, 337, 353, 367, 373, 379, 383, 401, 409, 431, 433, 439, 443, 449, 463, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 571, 577

Offset: 1

Robert Price, Nov 14 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. However, in base 2 we adopt the convention that 2 = 10 and 3 = 11 are deletable.
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 A096246.

Robert Price, Table of n, a(n) for n = 1..2351

Cf. A080608, A080603, A096235-A096246.

d = {2, 3};
For[n = 3, n <= 15, n++,
  p = Select[Range[2^(n - 1), 2^n - 1], PrimeQ[#] &];
  For[i = 1, i <= Length[p], i++,
   c = IntegerDigits[p[[i]], 2];
   For[j = 1, j <= n, j++,
    t = Delete[c, j];
    If[t[[1]] == 0, Continue[]];
    If[MemberQ[d, FromDigits[t, 2]], AppendTo[d, p[[i]]];  Break[]]]]]; Complement[Table[Prime[n], {n, PrimePi[Last[d]]}], d]

A321658 Primes that are not base-4 deletable primes (written in base 10).

Original entry on oeis.org

5, 17, 37, 41, 73, 89, 97, 101, 131, 137, 149, 193, 199, 233, 257, 277, 281, 293, 313, 337, 347, 349, 353, 367, 373, 379, 389, 401, 409, 421, 521, 569, 577, 593, 601, 613, 617, 641, 661, 673, 677, 683, 761, 769, 809, 811, 823, 829, 853, 857, 859, 929, 937

Offset: 1

Robert Price, Nov 15 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 A319596.

Robert Price, Table of n, a(n) for n = 1..3741

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

b = 4; 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 06 2018 *)

cp's OEIS Frontend

A321910 Base-7 deletable primes (written in base 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A322173 Base-6 deletable primes (written in base 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A322471 Base-9 deletable primes (written in base 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A322474 Primes that are not base-10 deletable primes (written in base 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A322475 Base-11 deletable primes (written in base 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A322477 Base-12 deletable primes (written in base 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A096245 Number of n-digit base-12 deletable primes.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Python

Extensions

A320587 Primes that are not Base-3 deletable primes (written in base 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A321596 Primes that are not base-2 deletable primes (written in base 10).

Views

Author

Keywords

Comments