A371000 - OEIS

A371000

a(n) are the records of the number of addends of the form j*(j+1)/2 (A000217) producing a sequence of consecutive composites starting at A370999(n).

%I #12 Apr 30 2024 14:48:30

%S 0,1,3,6,9,12,15,21,27,33,45,87,99,102,123,156,246,273,282,330,429,

%T 465,477,561,681,891,1050,1206,1338,1443,1449,1479,1656,1701,1836,

%U 1899,1941,2151,2199,2280,2301,2517,2592,2595,2709,2724,2751,2760,2934,3045,3240,3333,3546,3576,3867,3984

%N a(n) are the records of the number of addends of the form j*(j+1)/2 (A000217) producing a sequence of consecutive composites starting at A370999(n).

%C The "Ponder This Challenge" of March 2024 asked for the smallest start value of sequences of at least 1000 (or 2024 to gain the bonus) composite numbers in a progression defined by A000217.

%H IBM Research, <a href="https://research.ibm.com/haifa/ponderthis/challenges/March2024.html">Composite Sequences</a>, Ponder This Challenge March 2024.

%o (PARI) a371000(upto) = {my(m=0); forcomposite (k=4, upto, for (j=1, oo, if (isprime(k+(j*(j+1))/2), if (j>m, print1(j-1, ", "); m=j); break)))};

%o a371000(10^7)

%Y Cf. A000217, A370999, A371001, A371002.

%K nonn

%O 1,3

%A _Karl-Heinz Hofmann_ and _Hugo Pfoertner_, Mar 09 2024