cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A361076 Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2*n-1)*2^k+1, if they exist and n > 1; and of zeros otherwise.

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%I A361076 #50 Apr 01 2023 23:57:01
%S A361076 1,1,2,1,2,4,2,3,5,8,1,4,7,6,16,1,2,6,13,8,32,2,3,3,14,15,12,64,1,8,5,
%T A361076 6,20,25,18,128,3,2,10,7,7,26,39,30,256,6,15,4,20,19,11,50,55,36,512,
%U A361076 1,10,27,9,28,21,14,52,75,41,1024,1,4,46,51,10,82,43,17,92,85,66,2048
%N A361076 Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2*n-1)*2^k+1, if they exist and n > 1; and of zeros otherwise.
%C A361076 Is a(n) <= A279709(n)?
%H A361076 Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/riesel1.html">List of primes k.2^n + 1 for k < 300</a>.
%e A361076 Table starts
%e A361076   1   2   4   8  16  32  64 128 ... A000079
%e A361076   1   2   5   6   8  12  18  30 ... A002253
%e A361076   1   3   7  13  15  25  39  55 ... A002254
%e A361076   2   4   6  14  20  26  50  52 ... A032353
%e A361076   1   2   3   6   7  11  14  17 ... A002256
%e A361076   1   3   5   7  19  21  43  81 ... A002261
%e A361076   2   8  10  20  28  82 188 308 ... A032356
%e A361076   1   2   4   9  10  12  27  37 ... A002258
%e A361076   ...
%e A361076 (2*39279 - 1)*2^r + 1 is composite for every r > 0 (see comments from A046067), so the 39279th row is A000004, the zero sequence.
%o A361076 (PARI) vk(k, nn) = if (k==1, return (vector(nn, i, 2^(i-1)))); my(v = vector(nn-k+1), nb=0, i=0, x); while (nb != nn-k+1, if (isprime((2*k-1)*2^i+1), nb++; v[nb] = i); i++;); v;
%o A361076 lista(nn) = my(v=vector(nn, k, vk(k, nn))); my(w=List()); for (i=1, nn, for (j=1, i, listput(w, v[i-j+1][j]););); Vec(w); \\ _Michel Marcus_, Mar 03 2023
%Y A361076 Cf. A000079, A002253, A002254, A032353, A002256, A002261, A032356, A002258.
%Y A361076 Cf. A033809 (1st column).
%Y A361076 Cf. A000004, A046067, A279709.
%K A361076 nonn,tabl
%O A361076 1,3
%A A361076 _Lorenzo Sauras Altuzarra_, Mar 01 2023