The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A320161 Irregular triangle read by rows: row n lists 0 <= k < p^2 such that p^2 divides A316269(k, p-Kronecker(k^2-4, p)), p = prime(n). 2
 0, 1, 3, 0, 1, 8, 0, 1, 24, 0, 1, 10, 39, 48, 0, 1, 27, 36, 37, 84, 85, 94, 120, 0, 1, 6, 29, 34, 61, 108, 135, 140, 163, 168, 0, 1, 25, 45, 56, 75, 82, 132, 157, 207, 214, 233, 244, 264, 288, 0, 1, 42, 43, 73, 88, 106, 120, 161, 200, 241, 255, 273, 288, 318, 319, 360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS p always divides A316269(k, p-Kronecker(k^2-4, p)), so it's interesting to see when p^2 also divides A316269(k, p-Kronecker(k^2-4, p)). In the following comments, let p = prime(n). Note that A316269(0, m) and A316269(1, m) is not defined, so here k must be understood as a remainder modulo p^2. because A316269(k+s*p^2, m) == A316269(k, m) (mod p^2). Let p = prime(n). Every row contains 0, 1 and p^2 - 1. For n >= 3, the n-th row contains p - 2 numbers, whose remainders modulo p form a permutation of {0, 1, 3, 4, ..., p - 3, p - 1}. Every row is antisymmetric, that is, k is a member iff p^2 - k is, k > 0. As a result, the sum of the n-th row is prime(n)^2*(prime(n) - 3)/2. Equivalently, for n >= 2, row n lists 0 <= k < p^2 such that p^2 divides A316269(k, (p-Kronecker(k^2-4, p))/2), p = prime(n). LINKS Jianing Song, Table of n, a(n) for n = 1..29083 (primes below 600) Jianing Song, Table of n, a(n) for n = 1..75796 (primes below 1000) Wikipedia, Wall-Sun-Sun prime EXAMPLE Table starts p = 2: 0, 1, 3, p = 3: 0, 1, 8, p = 5: 0, 1, 24, p = 7: 0, 1, 10, 39, 48, p = 11: 0, 1, 27, 36, 37, 84, 85, 94, 120, p = 13: 0, 1, 6, 29, 34, 61, 108, 135, 140, 163, 168, p = 17: 0, 1, 25, 45, 56, 75, 82, 132, 157, 207, 214, 233, 244, 264, 288, p = 19: 0, 1, 42, 43, 73, 88, 106, 120, 161, 200, 241, 255, 273, 288, 318, 319, 360, p = 23: 0, 1, 12, 15, 60, 86, 105, 141, 142, 156, 223, 306, 373, 387, 388, 424, 443, 469, 514, 517, 528, p = 29: 0, 1, 42, 46, 80, 101, 107, 120, 226, 227, 327, 330, 358, 409, 432, 483, 511, 514, 614, 615, 721, 734, 740, 761, 795, 799, 840, ... PROG (PARI) B(k, p) = (([k, -1; 1, 0]^(p-kronecker(k^2-4, p)))[1, 2])%(p^2) forprime(p=2, 50, for(k=0, p^2-1, if(!B(k, p), print1(k, ", "))); print) CROSSREFS Cf. A143548, A316269, A320162 (discriminant k^2+4, a more studied case). Cf. A238490 (primes p such that 4 occurs in the corresponding row), A238736 (primes p such that 6 occurs in the corresponding row). Sequence in context: A290776 A172249 A208758 * A291763 A161129 A011074 Adjacent sequences:  A320158 A320159 A320160 * A320162 A320163 A320164 KEYWORD nonn,tabf AUTHOR Jianing Song, Oct 06 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)