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.
Lorenzo Sauras Altuzarra's wiki page.
Lorenzo Sauras Altuzarra has authored 20 sequences. Here are the ten most recent ones:
Table starts 1 2 4 8 16 32 64 128 ... A000079 1 2 5 6 8 12 18 30 ... A002253 1 3 7 13 15 25 39 55 ... A002254 2 4 6 14 20 26 50 52 ... A032353 1 2 3 6 7 11 14 17 ... A002256 1 3 5 7 19 21 43 81 ... A002261 2 8 10 20 28 82 188 308 ... A032356 1 2 4 9 10 12 27 37 ... A002258 ... (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.
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; 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
641 = 5*2^7 + 1 is a term because 0 < 5 <= 7 and 5 is odd.
# Maple program (due to David A. Corneth) aList := proc(upto) local i, j, R: R := {}: for i from 1 to ilog2(upto) do for j from 1 to min(i, floor(upto/2^i)) do R := `union`(R, {j*2^i+1}): od: od: R: end: aList(10^12);
3 is a term because the odd part of 2 is 1, the dyadic valuation of 2 is 1 and 1 <= 1. 641 = 5*2^7 + 1 is a term because the odd part of 640 is 5, the dyadic valuation of 640 is 7 and 5 <= 7.
# Maple program due to David A. Corneth, Mar 03 2023 aList := proc(upto) local i, j, p, R: R := {}: for i from 1 to ilog2(upto) do for j from 1 to min(i, floor(upto/2^i)) do p := j*2^i+1: if isprime(p) then R := `union`(R, {p}): fi: od: od: R: end: aList(10^12);
isok(p) = if (isprime(p), my(m=valuation(p-1,2)); (p-1)/2^m <= m); \\ Michel Marcus, Mar 03 2023
upto(n) = {my(res = List()); for(i = 1, logint(n, 2), forstep(j = 1, min(i, n>>i), 2, if(isprime((j<David A. Corneth, Mar 03 2023
A093179(5) = 641, A007117(5) = 5 and the only k >= 0 such that, for every odd r > 0, 641 divides the generalized Fermat number (5^r)^(2^k) + 1 is 5; so a(5) = 5.
a:=n->n-padic:-ordp(n+2,2): seq(a(n), n=3..79);
a(n) = n - valuation(n+2, 2); vector(77,n,a(n+2)) \\ Joerg Arndt, Mar 03 2023
For n=5, the smallest prime factor of F(5) = 2^(2^5) + 1 is 641 and it falls between 2^(2^5 - 23) = 512 < 641 < 1024 = 2^(2^5 - 22) so that a(5) = 23.
311, 2111, 2711, 7211, and 9011 are terms of A001359.
terms := proc(n)
local k, p, L:
k, L := 0, []:
while numelems(L) < n do
k := k+1:
p := parse(cat(k, 11)):
if isprime(p) and isprime(p+2) then L := [op(L), k]: fi: od:
L: end:
Select[Range[1282], AllTrue[# + {0, 2}, PrimeQ] &[100 # + 11] &] (* Michael De Vlieger, Dec 21 2021 *)
from itertools import count, islice from sympy import isprime def A350247_gen(startvalue=3): # generator of terms >= startvalue for n in count(max(3,startvalue+(3-startvalue%3)%3),3): if isprime(100*n+11) and isprime(100*n+13): yield n A350247_list = list(islice(A350247_gen(),20)) # Chai Wah Wu, Jan 20 2022
11, 311, 18311, 1518311, and 421518311 are terms of A001359.
terms := proc(n)
local i, j, p, q, L, M:
i, L, M := 0, [11], [11]:
while numelems(L) < n do
i, j := i+1, 0:
while 1 > 0 do
j, p := j+1, M[numelems(M)]:
q := parse(cat(j, p)):
if isprime(q) and isprime(q+2) then
L, M := [op(L), j], [op(M), q]:
break: fi: od: od:
L: end:
from itertools import count, islice from sympy import isprime def A350246_gen(): # generator of terms yield 11 s = '11' while True: for k in count(3,3): t = str(k) m = int(t+s) if isprime(m) and isprime(m+2): yield k break s = t+s A350246_list = list(islice(A350246_gen(),20)) # Chai Wah Wu, Jan 12 2022
A023394(1) = 3 = A050922(0), so a(1) = 0. A023394(2) = 5 = A050922(1), so a(2) = 1.
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