A171376
Numbers k such that 1 + 3*10^k + 100^k is prime.
Original entry on oeis.org
0, 1, 2, 3, 4, 11, 14, 16, 92, 133, 153, 378, 448, 785, 1488, 1915, 2297, 3286, 4755, 5825, 7820, 34442, 34941
Offset: 1
4 is in the sequence because 10^8 + 3 * 10^4 + 1 = 100030001 is prime.
-
[n: n in [0..4*10^2] | IsPrime(1+3*10^n+100^n)]; // Vincenzo Librandi, Dec 22 2015
-
Select[Range@ 1000, PrimeQ[1 + 3 10^# + 100^#] &] (* Michael De Vlieger, Dec 18 2015 *)
-
\\sieve for the candidates:
{
lim=10^9; ns=6*10^5; pp=10^7; s=vectorsmall(ns);
forprime(p=11,lim,if(kronecker(5,p)==1,o=znorder(t=Mod(10,p));
q=sqrt(Mod(5,p));r=znlog((q-3)/2,t,o);
if(r,forstep(n=r,ns,o,s[n]=1);forstep(n=o-r,ns,o,s[n]=1)));
if(p>pp,pp+=10000000;print1(p" ")));
for(n=1,ns,if(!s[n],write("sieve_out_10301NGm1.txt", n)));
}
\\quick initial check for small sequence members
for(n=0,2297,if(ispseudoprime((10^n+3)*10^n+1),print1(n", ")))
\\ Serge Batalov, Dec 17 2015
A082620
a(1) = 1, then the smallest palindromic prime obtained by inserting digits anywhere in a(n-1).
Original entry on oeis.org
1, 11, 101, 10301, 1003001, 100030001, 10003630001, 1000136310001, 100010363010001, 10001036363010001, 1000103639363010001, 100010356393653010001, 10001033563936533010001, 1000103305639365033010001, 100010313056393650313010001, 10001031305636963650313010001
Offset: 1
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 29 2003
A082621
a(1) = 2, then the smallest palindromic prime obtained by inserting digits anywhere in a(n-1) (including at the ends).
Original entry on oeis.org
2, 727, 37273, 3072703, 307323703, 30073237003, 3006732376003, 300067323760003, 30000673237600003, 3000067382837600003, 300006738242837600003, 30000673820402837600003, 3000063738204028373600003, 300006373821040128373600003, 30000635738210401283753600003
Offset: 1
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 29 2003
A082623
a(1) = 5, a(n) = smallest palindromic prime obtained by inserting two digits anywhere in a(n-1).
Original entry on oeis.org
5, 151, 10501, 1035301, 103515301, 10325152301, 1013251523101, 101325181523101, 10132512821523101, 1013251428241523101, 101322514282415223101, 10132245142824154223101, 1013224514281824154223101, 101322451402818204154223101, 10132245014028182041054223101
Offset: 1
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 29 2003
-
cp:= proc(x,y) if x[1] < y[1] then true
elif x[1] > y[1] then false
elif nops(x)=1 then true
else procname(x[2..-1],y[2..-1])
fi
end proc: A[1]:= 5: L:= [5]:
for n from 2 to 15 do
nL:= nops(L);
Lp:= sort([seq(seq([op(L[1..i]), x, op(L[i+1..-1])], x=`if`(i=0, 1..9, 0..9)), i=0..nL)], cp);
cands:= map(t -> add(t[i]*(10^(i-1)+10^(2*nL+1-i)), i=1..nL)+t[nL+1]*10^(nL), Lp);
found:= false;
for i from 1 to nops(cands) do
if isprime(cands[i]) then
A[n]:= cands[i];
L:= Lp[i];
found:= true;
break
fi
od;
if not found then break fi
od:
seq(A[i],i=1..15); # Robert Israel, Jan 03 2017, corrected Sep 20 2019
A082624
a(1) = 7, a(n) = smallest palindromic prime obtained by inserting digit anywhere in a(n-1).
Original entry on oeis.org
7, 373, 30703, 3007003, 302070203, 30207570203, 3062075702603, 306020757020603, 30602075057020603, 3060320750570230603, 300603207505702306003, 30060320275057202306003, 3006032021750571202306003, 300603202127505721202306003, 30046032021275057212023064003
Offset: 1
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 29 2003
Showing 1-5 of 5 results.
Comments