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A253596 Numbers k such that A002313(m) is the greatest prime divisor of k^2 + 1 and A002313(m+1) is the greatest prime divisor of (k+1)^2 + 1 for some m. 0
1, 7, 31, 293, 1936, 2244, 4158, 5744, 11573, 25242, 285202, 339354 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A002313 contains the primes congruent to 1 or 2 (mod 4).
The corresponding indices m in A002313 are 1, 2, 6, 13, 69, 65, 322, 199, 130, 46, 1471, 866, ...
The corresponding primes A002313(m) are 2, 5, 37, 101, 809, 761, 4877, 2777, 1709, 509, 26821, 14957, ...
LINKS
EXAMPLE
31 is in the sequence because 31^2 + 1 = 2*13*37 and 32^2 + 1 = 5*5*41 with the property that 37 = A002313(6) and 41 = A002313(7).
MAPLE
with(numtheory): nn:=500000:print(1):
for n from 1 to nn do:
p:=n^2+1:x:=factorset(p):n0:=nops(x):p1:=x[n0]:
q:=(n+1)^2+1:y:=factorset(q):n1:=nops(y):p2:=y[n1]:ii:=0:
for j from 2 by 2 to 1000 while(ii=0) do:
pp:=p1+j:
if type(pp, prime)=true and irem(pp, 4)=1
then
p3:=pp:ii:=1:
else
fi:
od:
if p3=p2
then
print(n):
else
fi:
od:
MATHEMATICA
lst={}; Do[If[Mod[Prime[i], 4]==1||Mod[Prime[i], 4]==2, AppendTo[lst, Prime[i]]], {i, 1, 1000}]; Do[Do[If[FactorInteger[n^2+1][[-1]][[1]]==Part[lst, j]&&FactorInteger[(n+1)^2+1][[-1]][[1]]==Part[lst, j+1], Print[n]], {n, 1, 20000}], {j, 1, 999}]
CROSSREFS
Sequence in context: A143564 A352411 A344787 * A298958 A153028 A276667
KEYWORD
nonn,more
AUTHOR
Michel Lagneau, Jan 05 2015
STATUS
approved

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Last modified June 20 22:01 EDT 2024. Contains 373532 sequences. (Running on oeis4.)