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.
from sympy import prime, nextprime def A360311(n): p = prime(n) q = nextprime(p) s, k = p+q, 1 while s%(q:=nextprime(q)): k += 1 s += q return s # Chai Wah Wu, Feb 06 2023
from sympy import prime, nextprime def A360312(n): p = prime(n) q = nextprime(p) s, k = p+q, 1 while s%(q:=nextprime(q)): k += 1 s += q return q # Chai Wah Wu, Feb 06 2023
a(1) = 0 as prime(1) + 1 = 2 + 1 = 3, which is divisible by prime(2) = 3. a(3) = 14 as prime(3) * ... * prime(17) + 1 = 320460058359035439846, which is divisible by prime(18) = 61. a(10) = 277856 as prime(10) * ... * prime(277866) + 1 = 645399...451368 (a number with 1701172 digits), which is divisible by prime(277867) = 3919259. a(11) = 1 as prime(11) * prime(12) + 1 = 31 * 37 + 1 = 1148, which is divisible by prime(13) = 41.
from sympy import prime, nextprime def A360376(n): p = prime(n) s, k = p, 0 while (s+1)%(p:=nextprime(p)): k += 1 s *= p return k # Chai Wah Wu, Feb 07 2023
a(1) = 1 as prime(1) * prime(2) - 1 = 2 * 3 - 1 = 5, which is divisible by prime(3) = 5. a(2) = 1 as prime(2) * prime(3) - 1 = 3 * 5 - 1 = 14, which is divisible by prime(4) = 7. a(3) = 9 as prime(3) * ... * prime(12) - 1 = 1236789689134, which is divisible by prime(13) = 41.
f:= proc(n) local P,k,p; P:= ithprime(n); p:= nextprime(P); for k from 0 to 10^6 do if P-1 mod p = 0 then return k fi; p:= nextprime(p); od; FAIL end proc: map(f, [$1..8]); # Robert Israel, Feb 22 2023
from sympy import prime, nextprime def A360406(n): p = prime(n) q = nextprime(p) s, k = p*q, 1 while (s-1)%(q:=nextprime(q)): k += 1 s *= q return k # Chai Wah Wu, Feb 06 2023
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