A171765 -id:A171765 - cp's OEIS frontend

A074871 Start with n and repeatedly apply the map k -> T(k) = A053837(k) + A171765(k); a(n) is the number of steps (at least one) until a prime is reached, or 0 if no prime is ever reached.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 0, 1, 2, 2, 0, 1, 3, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 0, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 0, 1, 1, 2, 3, 1, 2, 1, 1, 0, 1, 1, 0, 1, 0

Offset: 1

Felice Russo, Sep 12 2002, Oct 11 2010

The first occurrence of k beginning with 0: 1, 2, 17, 59, 337, 779, 16999, 6888888, ..., . - Robert G. Wilson v, Oct 20 2010

			T(2)=2. So in one step we reach a prime.
T(3)=3 and then in one step again we reach a prime.
T(4)=4 and we will never reach a prime.
T(11)=1+2=3 and again in one step we reach a prime.
T(17)=7+8=15 --> T(15)=5+6=11 and then in two steps we reach a prime.
T(13)=3+4=7 and then 1 step......
T(14)=4+5=9 --> T(9)=9 --> T(9)=9........ and we will never reach a prime.

Cf. A053837, A171765. See A171772 for another version.

g[n_] := Block[{id = IntegerDigits@ n}, Mod[ Plus @@ id, 10] + If[n < 10, 0, Times @@ id]]; f[n_] := Block[{lst = Rest@ NestWhileList[g, n, UnsameQ, All]}, lsp = PrimeQ@ lst; If[ Last@ Union@ lsp == False, 0, Position[lsp, True, 1, 1][[1, 1]]]]; Array[f, 105] (* Robert G. Wilson v, Oct 20 2010 *)

Edited by N. J. A. Sloane, Oct 12 2010

More terms from Robert G. Wilson v, Oct 20 2010

A035930 Maximal product of any two numbers whose concatenation is n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 10, 20, 30, 40, 50, 60, 70

Offset: 0

Erich Friedman

Agrees up to a(100) = 0 with A088117, A171765 and A257297, but all of the four differ in a(101) and subsequent values. - M. F. Hasler, Sep 01 2021

			a(341) = max(34*1,3*41) = 123.

Alois P. Heinz, Table of n, a(n) for n = 0..9999
Eric Angelini, Surface of a number, Sep 01 2021.

Different from A007954, A088117, A171765 and A257297. Cf. A035931-A035935.

a035930 n | n < 10    = 0
          | otherwise = maximum $ zipWith (*)
            (map read $ init $ tail $ inits $ show n)
            (map read $ tail $ init $ tails $ show n)
-- Reinhard Zumkeller, Aug 14 2011

a:= proc(n) local l, m; l:= convert(n, base, 10); m:= nops(l);
      `if`(m<2, 0, max(seq(parse(cat(seq(l[m-i], i=0..j-1)))
       *parse(cat(seq(l[m-i], i=j..m-1))), j=1..m)))
    end:
seq(a(n), n=0..120);  # Alois P. Heinz, May 22 2009

Flatten[With[{c=Range[0,9]},Table[c*n,{n,0,10}]]] (* Harvey P. Dale, Jun 07 2012 *)

apply( {A035930(n)=if(n>9,vecmax([vecprod(divrem( n,10^j))|j<-[1..logint(n,10)]]))}, [0..111]) \\ M. F. Hasler, Sep 01 2021

def a(n):
    s = str(n)
    return max((int(s[:i])*int(s[i:]) for i in range(1, len(s))), default=0)
print([a(n) for n in range(108)]) # Michael S. Branicky, Sep 01 2021

An erroneous formula was deleted by N. J. A. Sloane, Dec 23 2008

A257850 a(n) = floor(n/10) * (n mod 10).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8

Offset: 0

M. F. Hasler, May 10 2015

Equivalently, write n in base 10, multiply the last digit by the number with its last digit removed.
See A142150(n-1) for the base 2 analog and A257843 - A257849 for the base 3 - base 9 variants.
The first 100 terms coincide with those of A035930 (maximal product of any two numbers whose concatenation is n), A171765 (product of digits of n, or 0 for n<10), A257297 ((initial digit of n)*(n with initial digit removed)), but the sequence is of course different from each of these three.
The terms a(10) - a(100) also coincide with those of A007954 (product of decimal digits of n).

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,-1).

Cf. A142150 (the base 2 analog), A115273, A257844 - A257849.

Cf. also A007954, A035930, A171765, A257297.

[Floor(n/10)*(n mod 10): n in [0..100]]; // Vincenzo Librandi, May 11 2015

Table[Floor[n/10] Mod[n, 10], {n, 100}] (* Vincenzo Librandi, May 11 2015 *)

PARI
```
a(n,b=10)=(n=divrem(n,b))[1]*n[2]
```

def A257850(n): return n//10*(n%10) # M. F. Hasler, Sep 01 2021

a(n) = 2*a(n-10)-a(n-20). - Colin Barker, May 11 2015

G.f.: x^11*(9*x^8+8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)^2*(x+1)^2*(x^4-x^3+x^2-x+1)^2*(x^4+x^3+x^2+x+1)^2). - Colin Barker, May 11 2015

A088117 Let the decimal expansion of n be abcd...; then a(n) = (abcd... + bacd... + cabd... + dabc... + ...) + (abcd... + bcad... + cdab... + ...) + ... . That is, a(n) = sum over all the digit strings of the product (number obtained by deleting a digit string) (deleted digit string).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 11

Offset: 0

Amarnath Murthy, Sep 25 2003

Each substring is used in only product.

a(n) = 0 for 0 <= n <= 10.

			a(1234) = (1*234 + 2*134 + 3*124 + 4*123) + (12*34 + 23*14) = 2096.
a(12345) = (1*2345 + 2*1345 + 3*1245 + 4*1235 + 5*1234) + (12*345 + 15*234 + 23*145 + 34*125 + 45*123) = 40650.

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Cf. A007954, A088116.

Different from A035930, A171765, A257850.

a:= n-> (s-> add(add(parse(s[i..j])*parse(cat(s[1..i-1],
    s[j+1..length(s)])), i=1..j), j=1..length(s)-1))(""||n):
seq(a(n), n=0..120);  # Alois P. Heinz, May 22 2021

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jul 14 2007

a(0)=0 inserted and examples corrected by Alois P. Heinz, May 22 2021

A257297 a(n) = (initial digit of n) * (n with initial digit removed).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 1, 2, 3

Offset: 0

M. F. Hasler, May 10 2015

The initial 100 terms match those of A035930 (maximal product of any two numbers whose concatenation is n) and also those of A171765 (product of digits of n, or 0 for n<10), and except for initial terms, also A007954 (product of decimal digits of n) and A115300 (greatest digit of n * least digit of n).
Iterations of this map always end in 0, since a(n) < n. Sequence A257299 lists numbers for which these iterations reach 0 in exactly 9 steps, with the additional constraint of having each time a different initial digit.
If "initial" is replaced by "last" in the definition (A257850), then we get the same values up to a(100), but (10, 20, 30, ...) for n = 101, 102, 103, ..., again different from each of the 4 other sequences mentioned in the first comment. - M. F. Hasler, Sep 01 2021

			For n<10, a(n) = n*0 = 0, since removing the initial and only digit leaves nothing, i.e., zero (by convention).
a(10) = 1*0 = 0, a(12) = 1*2 = 2, ..., a(20) = 2*0 = 0, a(21) = 2*1 = 2, a(22) = 2*2 = 4, ...
a(99) = 9*9 = 81, a(100) = 1*00 = 0, a(101) = 1*01 = 1, ..., a(123) = 1*23, ...

Cf. A257850, A007954, A035930, A080464, A115300, A169669, A111707, A088117, A187844.

a:= n-> `if`(n<10, 0, (s-> parse(s[1])*parse(s[2..-1]))(""||n)):
seq(a(n), n=0..120);  # Alois P. Heinz, Feb 12 2024

Table[Times@@FromDigits/@TakeDrop[IntegerDigits@n,1],{n,0,103}] (* Giorgos Kalogeropoulos, Sep 03 2021 *)

apply( {A257297(n)=vecprod(divrem(n,10^logint(n+!n,10)))}, [0..111]) \\ Edited by M. F. Hasler, Sep 01 2021

def a(n): s = str(n); return 0 if len(s) < 2 else int(s[0])*int(s[1:])
print([a(n) for n in range(104)]) # Michael S. Branicky, Sep 01 2021

For 1 <= m <= 9 and n < 10^k, a(m*10^k + n) = m*n.

a(101..103) corrected by M. F. Hasler, Sep 01 2021

A330633 The concatenation of the products of every pair of consecutive digits of n (with a(n) = 0 for 0 <= n <= 9).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0

Offset: 0

Scott R. Shannon, Dec 21 2019

If the decimal expansion of n is d_1 d_2 ... d_k then a(n) is the number formed by concatenating the decimal numbers d_1*d_2, d_2*d_3, ..., d_{k-1}*d_k.

Due to the fact that for two digit numbers the sequence is simply the multiplication of those two numbers, this sequence matches numerous others for the first 100 terms. See the sequences in the cross references. The terms begin to differ beyond n = 100.

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Cf. A007954, A088117, A040115, A053392, A035930, A257850, A080464, A171765, A169669, A257297.

read("transforms") :
A330633 := proc(n)
    local dgs,L,i ;
    if n <=9 then
        0;
    else
        dgs := ListTools[Reverse](convert(n,base,10)) ;
        L := [] ;
        for i from 2 to nops(dgs) do
            L := [op(L), op(i-1,dgs)*op(i,dgs)] ;
        end do:
        digcatL(L) ;
    end if;
end proc: # R. J. Mathar, Jan 11 2020

Array[If[Or[# == 0, IntegerLength@ # == 1], 0, FromDigits[Join @@ IntegerDigits[Times @@ # & /@ Partition[IntegerDigits@ #, 2, 1]]]] &, 81, 0] (* Michael De Vlieger, Dec 23 2019 *)

a(n) = my(d=digits(n), s="0"); for (k=1, #d-1, s=concat(s, d[k]*d[k+1])); eval(s); \\ Michel Marcus, Apr 28 2020

a(10) = 0 as 1 * 0 = 0.
a(29) = 18 as 2 * 9 = 18.
a(100) = 0 as 1 * 0 = 0 and 0 = 0 = 0, and '00' is reduced to 0.
a(110) = 10 as 1 * 1 = 1 and 1 * 0 = 0. This is the first term that differs from A007954 and A171765, the multiplication of all digits of n.

A172054 n-th number k such that 6k-1 is composite while 6k+1 is prime minus n-th number m such that 6m-1 is prime while 6m+1 is composite.

Original entry on oeis.org

2, 3, 4, 2, 6, 7, 5, 7, 8, 7, 9, 12, 12, 12, 9, 4, 6, 4, 8, 9, 7, 8, 12, 11, 14, 17, 17, 12, 18, 17, 19, 13, 13, 10, 11, 9, 8, 7, 15, 17, 18, 13, 12, 13, 13, 11, 11, 15, 19, 19, 23, 23, 19, 12, 16, 17, 12, 11, 18, 22, 27, 29, 27, 27, 25, 18, 27, 28, 23, 22, 23, 17, 21, 24, 23, 23, 30

Offset: 1

Juri-Stepan Gerasimov, Jan 24 2010

nonn

Are there negative terms?

The entries are positive for at least the first 250000 terms. - R. J. Mathar, May 22 2010

			The number 6 is the first integer k such that 6*k-1 is composite while 6*k+1 is prime, the number 4 is the first integer m such that 6*m -1 is prime while 6*m+1 is composite, so, 2 = 6 - 4 is the first term a(1) of this sequence. - _Bernard Schott_, Feb 18 2019

Muniru A Asiru, Table of n, a(n) for n = 1..20000

Cf. A121763, A171765.

L:=500;;
K:=Filtered([1..L],k-> not IsPrime(6*k-1) and IsPrime(6*k+1));;
M:=Filtered([1..L],m-> not IsPrime(6*m+1) and IsPrime(6*m-1));;
a:=List([1..Length(K)],i->K[i]-M[i]);; Print(a); # Muniru A Asiru, Feb 19 2019

A121765:=[n: n in [1..350] | not IsPrime(6*n-1) and  IsPrime(6*n+1)];
A121763:=[n: n in [1..350] | IsPrime(6*n-1) and not IsPrime(6*n+1)];
[A121765[n] - A121763[n]: n in [1..80]]; // G. C. Greubel, Feb 20 2019

A121765 := proc(n) option remember; if n = 1 then 6; else for a from procname(n-1)+1 do if 6*a-1 >=4 and not isprime(6*a-1) and isprime(6*a+1) then return a; end if; end do; end if; end proc:
A121763 := proc(n) option remember; if n = 1 then 4; else for a from procname(n-1)+1 do if 6*a+1 >=4 and not isprime(6*a+1) and isprime(6*a-1) then return a; end if; end do; end if; end proc:
A172054 := proc(n) A121765(n)-A121763(n) ; end proc:
seq(A172054(n),n=1..120) ; # R. J. Mathar, May 22 2010

A121765:= Select[Range[350], !PrimeQ[6#-1] && PrimeQ[6#+1] &];
A121763:= Select[Range[350], PrimeQ[6#-1] && !PrimeQ[6#+1] &];
Table[A121765[[n]] - A121763[[n]], {n, 1, 80}] (* G. C. Greubel, Feb 20 2019 *)

A121765=[n for n in (1..350) if not is_prime(6*n-1) and is_prime(6*n+1)];
A121763=[n for n in (1..350) if is_prime(6*n-1) and not is_prime(6*n+1)];
[A121765[n] - A121763[n] for n in (0..80)] # G. C. Greubel, Feb 20 2019

a(n) = A121765(n) - A121763(n).

Entries checked by R. J. Mathar, May 22 2010

A347470 Least product of any two numbers whose concatenation is n, excluding 0*n for n > 9.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 0, 11, 12

Offset: 0

M. F. Hasler, Sep 03 2021

Leading zeros are not allowed: e.g., 101 = concat(10,1) but not concat(1,01). Although 0 is a valid number, we don't allow the trivial decomposition n = concat(0, n) except for the single-digit n < 10, otherwise the minimal product would always be 0.

For n < 111, this sequence coincides with A035930 (same with "largest"), because there is only one possible concatenation, but it differs for n > 111, cf. examples.

			The number n = 112 is the concatenation of 1 and 12, or of 11 and 2, with respective products 1*12 = 12 and 11*2 = 22. Hence, a(112) = 12, while A035930(112) = 22.

Eric Angelini, Surface of a number, Sep 01 2021.

Cf. A035930, A007954, A088117, A171765 and A257297.

apply( {A347470(x,t(b,c)=if(c\10<=b%c,b\c*(b%c),c>10,oo))= if(x>9,vecmin(vector(logint(x,10),j,t(x,10^j))))}, [0..112])

A172055 n-th number k such that 6k-1 is composite while 6k+1 is prime plus n-th number m such that 6m-1 is prime while 6m+1 is composite.

Original entry on oeis.org

10, 19, 22, 30, 36, 45, 49, 63, 66, 85, 93, 98, 100, 110, 115, 122, 126, 132, 138, 143, 155, 158, 168, 171, 178, 185, 187, 198, 206, 213, 217, 229, 231, 236, 239, 243, 248, 255, 269, 275, 284, 293, 300, 309, 317, 321, 325, 331, 337, 343, 349, 351, 357, 378

Offset: 1

Juri-Stepan Gerasimov, Jan 24 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A121763, A171765, A172054.

A121765:=Filtered([1..350],k-> not IsPrime(6*k-1) and IsPrime(6*k+1));;
A121763:=Filtered([1..350],n-> not IsPrime(6*n+1) and IsPrime(6*n-1));;
Print(List([1..80],j->A121765[j]+A121763[j])); # G. C. Greubel, Feb 20 2019

A121765:=[n: n in [1..350] | not IsPrime(6*n-1) and  IsPrime(6*n+1)];
A121763:=[n: n in [1..350] | IsPrime(6*n-1) and not IsPrime(6*n+1)];
[A121765[n] + A121763[n]: n in [1..80]]; // G. C. Greubel, Feb 20 2019

A121765:=select(k->not isprime(6*k-1) and isprime(6*k+1),[$1..350]):
A121763:=select(n->not isprime(6*n+1) and isprime(6*n-1),[$1..350]):
seq(A121765[m]+A121763[m],m=1..60); # Muniru A Asiru, Feb 21 2019

A121765:= Select[Range[350], !PrimeQ[6#-1] && PrimeQ[6#+1] &];
A121763:= Select[Range[350], PrimeQ[6#-1] && !PrimeQ[6#+1] &];
Table[A121765[[n]] + A121763[[n]], {n, 1, 80}] (* G. C. Greubel, Feb 20 2019 *)

A121765=[n for n in (1..350) if not is_prime(6*n-1) and is_prime(6*n+1)];
A121763=[n for n in (1..350) if is_prime(6*n-1) and not is_prime(6*n+1)];
[A121765[n] + A121763[n] for n in (0..80)] # G. C. Greubel, Feb 20 2019

a(n) = A121765(n) + A121763(n).

Entries checked by R. J. Mathar, May 22 2010

cp's OEIS Frontend

A074871 Start with n and repeatedly apply the map k -> T(k) = A053837(k) + A171765(k); a(n) is the number of steps (at least one) until a prime is reached, or 0 if no prime is ever reached.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A035930 Maximal product of any two numbers whose concatenation is n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Extensions

A257850 a(n) = floor(n/10) * (n mod 10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

Formula

A088117 Let the decimal expansion of n be abcd...; then a(n) = (a*bcd... + b*acd... + c*abd... + d*abc... + ...) + (ab*cd... + bc*ad... + cd*ab... + ...) + ... . That is, a(n) = sum over all the digit strings of the product (number obtained by deleting a digit string) * (deleted digit string).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Extensions

A257297 a(n) = (initial digit of n) * (n with initial digit removed).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

Extensions

A330633 The concatenation of the products of every pair of consecutive digits of n (with a(n) = 0 for 0 <= n <= 9).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A172054 n-th number k such that 6*k-1 is composite while 6*k+1 is prime minus n-th number m such that 6*m-1 is prime while 6*m+1 is composite.

Views

Author

Keywords

A088117 Let the decimal expansion of n be abcd...; then a(n) = (abcd... + bacd... + cabd... + dabc... + ...) + (abcd... + bcad... + cdab... + ...) + ... . That is, a(n) = sum over all the digit strings of the product (number obtained by deleting a digit string) (deleted digit string).

A172054 n-th number k such that 6k-1 is composite while 6k+1 is prime minus n-th number m such that 6m-1 is prime while 6m+1 is composite.

A172055 n-th number k such that 6k-1 is composite while 6k+1 is prime plus n-th number m such that 6m-1 is prime while 6m+1 is composite.