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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). 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn,tabl
AUTHOR
Amarnath Murthy, Jun 02 2004
EXTENSIONS
Edited and extended by Klaus Brockhaus, Jun 03 2004
STATUS
approved

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Last modified February 23 18:28 EST 2024. Contains 370283 sequences. (Running on oeis4.)