

A114920


Triangle where a(0,0) = 1; a(n,m) = number of terms in row (n1) which, when added to m, are primes.


4



1, 0, 1, 0, 1, 2, 1, 2, 2, 2, 3, 4, 1, 3, 1, 2, 3, 4, 1, 4, 0, 2, 4, 3, 4, 2, 2, 1, 4, 6, 2, 5, 2, 3, 1, 2, 5, 6, 3, 4, 2, 4, 2, 2, 2, 6, 7, 2, 6, 1, 5, 1, 3, 2, 6, 5, 7, 4, 2, 4, 5, 4, 3, 2, 2, 4, 7, 7, 3, 7, 2, 3, 3, 4, 3, 7, 2, 3, 11, 3, 5, 3, 9, 2, 4, 1, 5, 3, 9, 2, 4, 8, 5, 9, 4, 6, 2, 4, 2, 8, 4, 6, 2, 4, 2
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OFFSET

0,6


LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..11627 (rows 0 <= n <= 150).


EXAMPLE

Row 3 of the triangle is [1,2,2,2]. Adding 0 to these gives [1,2,2,2], of which 3 terms are primes. Adding 1 to these gives [2,3,3,3], of which 4 terms are primes. Adding 2 to these gives [3,4,4,4], of which one term is prime. Adding 3 to these gives [4,5,5,5], of which 3 terms are primes. Adding 4 to these gives [5,6,6,6], of which one term is prime. So row 4 is [3,4,1,3,1].
Triangle begins:
1;
0, 1;
0, 1, 2;
1, 2, 2, 2;
3, 4, 1, 3, 1;
2, 3, 4, 1, 4, 0;
2, 4, 3, 4, 2, 2, 1;
...


MATHEMATICA

NestList[Function[w, Map[Function[k, Count[Map[k + # &, w], _?PrimeQ]], Range[0, Length@ w]]], {1}, 13] // Flatten (* Michael De Vlieger, Sep 07 2017 *)


PROG

(PARI) {v=[1]; for(k=1, 20, w=vector(length(v)+1); for(i=0, length(v), for(j=1, length(v), if(isprime(v[j]+i), w[i+1]++))); v=w; print(v))} \\ Lambert Herrgesell(zero815(AT)googlemail.com), Jan 13 2006


CROSSREFS

Cf. A114919, A114905, A114906.
Sequence in context: A123505 A320779 A356876 * A283190 A030361 A060715
Adjacent sequences: A114917 A114918 A114919 * A114921 A114922 A114923


KEYWORD

nonn,tabl


AUTHOR

Leroy Quet, Jan 07 2006


EXTENSIONS

More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Jan 13 2006


STATUS

approved



