|
| |
|
|
A089395
|
|
Prime productive numbers n: Let the digits of n be abcd. Then the numbers bcd*a+1, cd*ab+1, d*abc+1, abcd+1 etc. are all primes. If n is a k-digit number it produces k such primes.
|
|
3
|
|
|
|
1, 2, 4, 6, 12, 16, 22, 28, 36, 52, 58, 66, 82, 106, 112, 136, 166, 178, 256, 306, 336, 352, 448, 502, 508, 556, 562, 586, 616, 652, 658, 718, 982, 1018, 1108, 1162, 1192, 1228, 1498, 1708, 2002, 2026, 2086, 2686, 2776, 2998, 3136, 3412, 3526, 3592, 4078, 4918
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Conjecture: Sequence is infinite.
|
|
|
LINKS
|
Table of n, a(n) for n=0..51.
|
|
|
EXAMPLE
|
256 is a member as 2*56 +1 = 113, 25*6 +1 = 151 and 256+1 = 257 are all primes.
|
|
|
MAPLE
|
with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1), j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1, op(i), d+1], i=[[], seq([j], j=2..d)])]: for n from 10^(d-1) to 10^d-1 do sn:=convert(n, base, 10): fl:=0: for s in sch do m:=mul(j, j=[seq(ds(sn[s[i]..s[i+1]-1]), i=1..nops(s)-1)])+1: if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, ", n) fi od od: (C. Ronaldo)
|
|
|
CROSSREFS
|
Cf. A089392, A089393, A089394, A089396, A089397.
Sequence in context: A090748 A188047 A032465 * A089699 A089696 A171609
Adjacent sequences: A089392 A089393 A089394 * A089396 A089397 A089398
|
|
|
KEYWORD
|
base,nonn
|
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 10 2003
|
|
|
EXTENSIONS
|
Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004
|
|
|
STATUS
|
approved
|
| |
|
|
