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.

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

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 14 2009

Keywords

• nonn
• base

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.

Examples

			19: 1319 and 1913 are primes => a(2)=19;
7 is not a term: 137 is prime but 713=23 * 31 is not.
		

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

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A157772.

Programs

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 *)