|
| |
|
|
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
|
|
3
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
1) It is conjectured and numerically examined that sequences of this type are infinite 2) It is also conjectured, that an infinite number of primes are member 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, Birkhaeuser 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
|
|
|
EXAMPLE
|
examples: 1) 19: 1319 and 1913 are primes => a(2)=19 2) 7 is no member: 137 is prime but 713=23 x 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) ; [From 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: A089837 A020347 A054864 * A178889 A167998 A050714
Adjacent sequences: A158229 A158230 A158231 * A158233 A158234 A158235
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 14 2009
|
|
|
STATUS
|
approved
|
| |
|
|
