A089395 Prime productive numbers m: Let the digits of m be abcd. Then the numbers bcd*a+1, cd*ab+1, d*abc+1, abcd+1 etc. are all primes. If m is a k-digit number it produces k such primes.

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

Offset

0,2

Comments

Conjecture: Sequence is infinite.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..139 (all terms up to 1 million)

Example

256 is a term 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

Mathematica

ppnQ[n_]:=Mod[n, 10]!=0&&AllTrue[Times@@@Table[FromDigits/@TakeDrop[ IntegerDigits[ n], k]/.(0->1), {k, IntegerLength[n]}]+1, PrimeQ]; Select[Range[5000], ppnQ] (* The program uses the AllTrue and TakeDrop functions from Mathematica version 10 *) (* Harvey P. Dale, Mar 23 2019 *)

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, Nov 10 2003

Extensions

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

Status

approved