A108841
Palindromic primes in which all internal digits are 4.
Original entry on oeis.org
1444441, 3444443, 74444444447, 3444444444443, 7444444444444444444444444444447, 1444444444444444444444444444444444444444444444444444444444444444441
Offset: 1
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select(isprime, [seq(seq(x*(10^d+1)+40*(10^(d-1)-1)/9,x=1..9,2),d=2..66)]); # Robert Israel, Oct 25 2018
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Sort[Select[FromDigits/@Flatten[Table[Join[{n},PadRight[{},i,4],{n}],{n,{1,3,7,9}},{i,150}],1],PrimeQ]] (* Harvey P. Dale, Nov 26 2014 *)
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n10np1(n,d) = { local(x,y,k); for(x=1,n, for(k=1,8, y=10^(x+1)*k+floor(10^x*d/9)*10+k; if(isprime(y),print1(y",")) ) ) }
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from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for f in "1379" if isprime(t:=int(f + "4"*i + f)))
print(list(islice(agen(), 9))) # Michael S. Branicky, Jan 27 2023
A108842
Palindromic primes in which all internal digits are 5.
Original entry on oeis.org
151, 353, 757, 15551, 75557, 355555553, 75555555557, 155555555555555555551, 755555555555555555557, 75555555555555555555557, 155555555555555555555555555555551, 75555555555555555555555555555555555555555555555555555555557
Offset: 1
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Select[Sort[Flatten[Table[FromDigits[Join[{n},PadRight[{},i,5],{n}]],{n,{1,3,7,9}},{i,80}]]],PrimeQ] (* Harvey P. Dale, May 18 2015 *)
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n10np1(n,d) = { local(x,y,k); for(x=1,n, for(k=1,8, y=10^(x+1)*k+floor(10^x*d/9)*10+k; if(isprime(y),print1(y",")) ) ) }
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from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for f in "1379" if isprime(t:=int(f + "5"*i + f)))
print(list(islice(agen(), 10))) # Michael S. Branicky, Jan 27 2023
A108843
Palindromic primes in which all internal digits are 6.
Original entry on oeis.org
16661, 76667, 7666667, 1666666666661, 16666666666666661, 1666666666666666661, 1666666666666666666666666666666666661, 16666666666666666666666666666666666666666666666666661
Offset: 1
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nn=80;With[{o=Table[FromDigits[Join[PadRight[{1},n,6],{1}]],{n,3,nn}], s= Table[ FromDigits[Join[PadRight[{7},n,6],{7}]],{n,3,nn}]}, Select[ Sort[ Join[o,s]],PrimeQ]] (* Harvey P. Dale, May 26 2014 *)
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n10np1(n,d) = { local(x,y,k); for(x=1,n, for(k=1,8, y=10^(x+1)*k+floor(10^x*d/9)*10+k; if(isprime(y),print1(y",")) ) ) }
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from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for f in "17" if isprime(t:=int(f + "6"*i + f)))
print(list(islice(agen(), 10))) # Michael S. Branicky, Jan 27 2023
A108845
Palindromic primes in which all internal digits are 1.
Original entry on oeis.org
313, 919, 3111111111113, 311111111111113, 1111111111111111111, 11111111111111111111111, 3111111111111111111111111111113
Offset: 1
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n10np1(n,d) = { local(x,y,k); for(x=1,n, for(k=1,9, y=10^(x+1)*k+floor(10^x*d/9)*10+k; if(isprime(y),print1(y",")) ) ) }
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from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for f in "1379" if isprime(t:=int(f + "1"*i + f)))
print(list(islice(agen(), 10))) # Michael S. Branicky, Jan 27 2023
A108846
Palindromic primes in which all internal digits are 2.
Original entry on oeis.org
727, 929, 72227, 3222223, 9222229, 322222223, 722222227, 9222222222229, 72222222222222222222222222227, 72222222222222222222222222222222222222222222222222222222222222227
Offset: 1
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Select[Flatten[Table[10 FromDigits[PadRight[{d},n,2]]+d,{d,{1,3,7,9}},{n,2,70}]],PrimeQ]//Sort (* Harvey P. Dale, Feb 05 2023 *)
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n10np1(n,d) = { local(x,y,k); for(x=1,n, for(k=1,9, y=10^(x+1)*k+floor(10^x*d/9)*10+k; if(isprime(y),print1(y",")) ) ) }
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from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for f in "1379" if isprime(t:=int(f + "2"*i + f)))
print(list(islice(agen(), 10))) # Michael S. Branicky, Jan 27 2023
A108847
Palindromic primes in which all internal digits are 8.
Original entry on oeis.org
181, 383, 787, 78887, 9888889, 188888881, 3888888888883, 188888888888881, 3888888888888888888888888888883, 18888888888888888888888888888888888888881
Offset: 1
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n10np1(n,d) = { local(x,y,k); for(x=1,n, for(k=1,9, y=10^(x+1)*k+floor(10^x*d/9)*10+k; if(isprime(y),print1(y",")) ) ) }
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from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for f in "1379" if isprime(t:=int(f + "8"*i + f)))
print(list(islice(agen(), 10))) # Michael S. Branicky, Jan 27 2023
A108848
Palindromic primes in which all internal digits are 9.
Original entry on oeis.org
191, 797, 19991, 79997, 199999991, 79999999999999999999999999997, 19999999999999999999999999999999999999991, 199999999999999999999999999999999999999999999999999999999999999999999999999999999999991
Offset: 1
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Select[Flatten[Table[FromDigits[PadRight[{k},n,9]]*10+k,{n,2,200},{k,{1,7}}]],PrimeQ] (* Harvey P. Dale, Dec 11 2019 *)
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n10np9(n,d) = { local(x,y,k); for(x=1,n, for(k=1,9, y=10^(x+1)*k+(10^x-1)*10+k; if(isprime(y),print1(y",")) ) ) }
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from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for f in "17" if isprime(t:=int(f + "9"*i + f)))
print(list(islice(agen(), 13))) # Michael S. Branicky, Jan 27 2023
A298729
Prime numbers whose decimal expansion includes a substring of seven consecutive 7's.
Original entry on oeis.org
137777777, 177777773, 177777779, 197777777, 307777777, 347777777, 437777777, 527777777, 547777777, 577777777, 587777777, 647777777, 697777777, 777777701, 777777739, 777777743, 777777751, 777777799, 787777777, 827777777, 947777777, 967777777, 1247777777, 1277777771, 1277777773, 1457777777, 1487777777
Offset: 1
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s = {7, 7, 7, 7, 7, 7, 7}; lst = {}; k = 1; While[k < 10001, l = 1; il = 12;
While[l < il, p = FromDigits@ Flatten@ Insert[ IntegerDigits[k, 10, 10], s, l];
If[PrimeQ@ p, AppendTo[lst, p]]; l++]; k++]; Union@ lst (* Robert G. Wilson v, Feb 08 2018 *)
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is(n) = my(v=vector(7, x, 7), d=digits(n)); for(k=1, #d-6, if([d[k], d[k+1], d[k+2], d[k+3], d[k+4], d[k+5], d[k+6]]==v, return(1))); 0
forprime(p=1, , if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Mar 06 2018
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