A095181 Triangle read by rows in which the j-th row begins with prime(j) and is the arithmetic progression with least common difference such that the remaining j-1 terms are composite and not divisible by prime(j).

2, 3, 4, 5, 16, 27, 7, 8, 9, 10, 11, 18, 25, 32, 39, 13, 24, 35, 46, 57, 68, 17, 64, 111, 158, 205, 252, 299, 19, 44, 69, 94, 119, 144, 169, 194, 23, 40, 57, 74, 91, 108, 125, 142, 159, 29, 81, 133, 185, 237, 289, 341, 393, 445, 497, 31, 54, 77, 100, 123, 146, 169, 192, 215

Offset

1,1

Links

Table of n, a(n) for n=1..64.

Example

2
3 4
5 16 27
7 8 9 10
11 18 25 32 39
13 24 35 46 57 68

Mathematica

row[n_] := For[r = 1, True, r++, ro = Table[Prime[n] + k*r, {k, 0, n-1}]; If[AllTrue[Rest[ro], CompositeQ[#] && !Divisible[#, Prime[n]]&], Return[ro] ] ]; Table[row[n], {n, 1, 11}] // Flatten (* Jean-François Alcover, Sep 26 2017 *)

Prog

(PARI) {check(p, j, a)=local(b, k); b=1; k=1; while(b&&k<j, x=p+a*k; if(isprime(x)||x%p==0, b=0, k++)); b}
{arithprog(p, j)=local(a); a=1; while(!check(p, j, a), a++); a}
{m=11; for(j=1, m, p=prime(j); d=arithprog(p, j); for(k=1, j, print1(p+d*(k-1), ", ")))}

Crossrefs

Cf. A095182.

Row sums are in A160915. [From Klaus Brockhaus, May 30 2009]

Sequence in context: A075687 A283526 A293824 * A240906 A117885 A030574

Adjacent sequences: A095178 A095179 A095180 * A095182 A095183 A095184

Keyword

nonn,tabl

Author

Amarnath Murthy, Jun 02 2004

Extensions

Edited and extended by Klaus Brockhaus, Jun 03 2004

Status

approved