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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. 4
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
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
Sequence in context: A090748 A188047 A032465 * A089699 A089696 A171609
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

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Last modified July 14 12:35 EDT 2024. Contains 374318 sequences. (Running on oeis4.)