login
A158232
Numbers which yield primes when "13" is prefixed or appended: N natural number is a member of the sequence, if P="13N" (prefixed 13) and A="N13" (appended 13) are prime.
11
1, 19, 21, 27, 61, 103, 121, 127, 147, 159, 177, 183, 187, 217, 241, 259, 267, 327, 331, 337, 367, 381, 411, 477, 523, 553, 567, 577, 591, 633, 681, 687, 693, 709, 723, 759, 807, 829, 873, 903, 931, 997, 1009, 1011, 1041, 1059, 1129, 1149, 1213, 1231, 1251
OFFSET
1,2
COMMENTS
It is conjectured and numerically examined that sequences of this type are infinite.
It is also conjectured that an infinite number of primes are terms of the sequence; first 20 primes are: 19, 61, 103, 127, 241, 331, 337, 367, 523, 577, 709, 829, 997, 1009, 1129, 1213, 1381, 1489, 1543, 1627.
REFERENCES
A. Weil, Number theory: an approach through history, Birkhäuser, 1984.
Richard E. Crandall, Carl Pomerance, Prime Numbers, Springer 2005.
Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996.
LINKS
EXAMPLE
19: 1319 and 1913 are primes => a(2)=19;
7 is not a term: 137 is prime but 713=23 * 31 is not.
MAPLE
A055642 := proc(n) max(1, ilog10(n)+1) ; end proc: cat2 := proc(a, b) a*10^A055642(b)+b ; end proc: A158232 := proc(n) option remember; local a; if n = 1 then 1; else for a from procname(n-1)+1 do if isprime(cat2(13, a)) and isprime(cat2(a, 13)) then return a ; end if ; end do ; end if; end proc: seq(A158232(n), n=1..80) ; # R. J. Mathar, Nov 11 2009
MATHEMATICA
Select[Range[1300], And@@PrimeQ[{13 10^IntegerLength[#]+#, 100#+13}]&] (* Harvey P. Dale, May 28 2012 *)
CROSSREFS
Cf. A157772.
Sequence in context: A334103 A347343 A054864 * A178889 A167998 A050714
KEYWORD
nonn,base
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 14 2009
STATUS
approved