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A069687 Primes that yield another prime on placing a 1 on both sides (as leading and trailing digits). 11

%I #25 Aug 22 2015 19:43:37

%S 3,5,17,23,29,47,53,83,107,113,131,149,173,197,239,251,317,359,383,

%T 401,443,503,509,599,641,683,701,719,743,797,821,947,953,1031,1049,

%U 1103,1109,1187,1229,1277,1283,1301,1373,1583,1613,1619,1637,1733,1847,1889

%N Primes that yield another prime on placing a 1 on both sides (as leading and trailing digits).

%H Harvey P. Dale, <a href="/A069687/b069687.txt">Table of n, a(n) for n = 1..1000</a>

%e 239 belongs to this sequence as 12391 is also a prime.

%e 947 and 19471 are both primes ==> 947 is in the sequence. [From _José María Grau Ribas_, Jan 22 2012]

%p a:= proc(n) option remember; local p;

%p p:= `if`(n=1, 1, a(n-1));

%p do p:= nextprime(p);

%p if isprime(parse(cat(1, p, 1))) then break fi

%p od; p

%p end:

%p seq(a(n), n=1..100); # _Alois P. Heinz_, May 18 2012

%t Select[ Range[2000], PrimeQ[ # ] && PrimeQ[ FromDigits[ Insert[ IntegerDigits[ # ], 1, {{1}, {-1}}]]] &]

%t san[i_]:=1+Prime[i]*10+10^(Floor@Log[10,Prime[i]]+2); Prime@Select[Range[1000],PrimeQ@san[#]&] (* From _José María Grau Ribas_, Jan 22 2012 *)

%t Select[Prime[Range[300]],PrimeQ[FromDigits[Join[{1},IntegerDigits[#],{1}]]]&] (* _Harvey P. Dale_, May 18 2012 *)

%o (PARI) forprime( p=1,9999, isprime(10^#Str(p*10)+p*10+1) & print1(p",")) \\ _M. F. Hasler_, May 18 2012

%o (PARI) A069687_vec(Nmax=10^4)=my(p,d=1);vector(Nmax,i,until(isprime((d+p)*10+1), d<(p=nextprime(p+1))&d*=10);p) \\ _M. F. Hasler_, May 19 2012

%Y Cf. A069688, A069689 & A069690.

%K nonn,base

%O 1,1

%A _Amarnath Murthy_, Apr 06 2002

%E Edited and extended by _Robert G. Wilson v_, May 03 2002

%E Corrected and edited following suggestions by H. P. Dale and others by _M. F. Hasler_, May 18 2012

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)