A069246 - OEIS

%I #30 Feb 24 2024 01:02:47

%S 3,7,13,31,103,109,151,181,193,367,571,601,613,811,1117,1831,4519,

%T 6871,11119,11317,11467,13171,16141,17167,18211,18457,27241,38917,

%U 55381,71317,81199,81931,86743,114031,139861,141667,151687,179203,200191

%N Primes which yield a prime whenever a 1 is inserted anywhere in them (including at the beginning or end).

%H Giovanni Resta, <a href="/A069246/b069246.txt">Table of n, a(n) for n = 1..270</a> (terms 1..77 from Vincenzo Librandi, terms 78..145 from Zak Seidov)

%t d[n_]:=IntegerDigits[n]; ins[n_]:=FromDigits/@Table[Insert[d[n],1,k],{k,Length[d[n]]+1}]; Select[Prime[Range[20000]],And@@PrimeQ/@ins[#] &] (* _Jayanta Basu_, May 20 2013 *)

%o (Magma) [p: p in PrimesUpTo(210000) | forall{m: t in [0..#Intseq(p)] | IsPrime(m) where m is (Floor(p/10^t)*10+1)*10^t+p mod 10^t}]; // _Bruno Berselli_, Sep 03 2012

%Y Prime subsequence of A068679.

%Y Cf. A215417, A215419 - A215421.

%K nonn,easy,base

%O 1,1

%A _N. J. A. Sloane_, Apr 14 2002

%E More terms from _Vladeta Jovovic_, Apr 16 2002