A217063 -id:A217063 - cp's OEIS frontend

A217062 Primes that remain prime when a single "9" digit is inserted between any two adjacent digits.

11, 13, 17, 19, 23, 37, 41, 53, 59, 61, 97, 101, 107, 113, 149, 193, 197, 199, 227, 239, 263, 269, 271, 311, 331, 367, 409, 431, 443, 457, 499, 587, 617, 659, 661, 691, 727, 733, 751, 823, 863, 941, 967, 1009, 1423, 1571, 1709, 1759, 1973, 1993, 1997, 2063, 2137

Offset: 1

Paolo P. Lava, Sep 26 2012

			214883 is prime and also 2148893, 2148983, 2149883, 2194883 and 2914883.

Paolo P. Lava, Table of n, a(n) for n = 1..236

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217047, A217063-A217065

with(numtheory);
A217062:=proc(q,x)
local a,b,c,i,n,ok;
for n from 5 to q do
  a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1;
    for i from 1 to b-1 do
      c:=a+9*10^i*trunc(a/10^i)+10^i*x;  if not isprime(c) then ok:=0; break; fi; od;
    if ok=1 then print(ithprime(n)); fi; od; end:
A217062(1000000,9);

is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=9; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012

A217064 Primes that remain prime when a single "5" digit is inserted between any two adjacent decimal digits.

Original entry on oeis.org

11, 17, 47, 71, 83, 89, 149, 167, 179, 251, 257, 293, 347, 359, 383, 419, 461, 467, 491, 557, 563, 569, 653, 773, 911, 1193, 1217, 1277, 1451, 1559, 1667, 1823, 1901, 2243, 2309, 2357, 2579, 2657, 2999, 3527, 3533, 4289, 5051, 5351, 5501, 5843, 6089, 6551, 6581

Offset: 1

Paolo P. Lava, Sep 26 2012

			290183 is prime and also 2901853, 2901583, 2905183, 2950183 and 2590183.

Harvey P. Dale, Table of n, a(n) for n = 1..500 (First 140 terms from Paolo P. Lava)

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217047, A217062, A217063, A217065

with(numtheory);
A217064:=proc(q,x)
local a,b,c,i,n,ok;
for n from 5 to q do
  a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1;
    for i from 1 to b-1 do
      c:=a+9*10^i*trunc(a/10^i)+10^i*x;  if not isprime(c) then ok:=0; break; fi; od;
    if ok=1 then print(ithprime(n)); fi; od; end:
A217064(1000000,5);

Select[Prime[Range[5,1000]],AllTrue[FromDigits/@Table[ Insert[ IntegerDigits[ #],5,n],{n,2,IntegerLength[#]}],PrimeQ]&] (* Harvey P. Dale, Feb 20 2022 *)

is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=5; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012

A349636 Primes that remain prime when a single "1" digit is inserted between any two adjacent digits.

Original entry on oeis.org

13, 31, 37, 67, 79, 103, 109, 151, 163, 181, 193, 211, 241, 367, 457, 547, 571, 601, 613, 631, 709, 787, 811, 1117, 1213, 1831, 2017, 2683, 3019, 3319, 3391, 3511, 3517, 3607, 4519, 4999, 6007, 6121, 6151, 6379, 6673, 6871, 6991, 8293, 11119, 11317, 11467

Offset: 1

Michael S. Branicky, Nov 23 2021

			37 and 317 are prime; 2683 is prime, as are 21683, 26183, and 26813.

Martin Ehrenstein, Table of n, a(n) for n = 1..2004

The terms of A069246 > 10 are a subsequence.
Cf. A215417 (same with 0), A217044 (2), A217045 (4), A217046 (6), A217047 (8), A217062 (9), A217063 (3), A217064 (5), A217065 (7).
Subsequence of A002476.

Select[Prime@Range[5,1500],(p=#;And@@PrimeQ[FromDigits/@(Insert[IntegerDigits@p,1,#]&/@Range[2,IntegerLength@p])])&] (* Giorgos Kalogeropoulos, Nov 23 2021 *)

from sympy import isprime, primerange
def ok(p):
    if p < 10: return False
    s = str(p)
    return all(isprime(int(s[:i] + "1" + s[i:])) for i in range(1, len(s)))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(12000)) # Michael S. Branicky, Nov 23 2021

cp's OEIS Frontend

A217062 Primes that remain prime when a single "9" digit is inserted between any two adjacent digits.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

PARI

A217064 Primes that remain prime when a single "5" digit is inserted between any two adjacent decimal digits.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A349636 Primes that remain prime when a single "1" digit is inserted between any two adjacent digits.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Python