OFFSET
1,1
COMMENTS
Conjecture: If the condition holds, prime(n-1) and prime(n) are twin primes of the form 10k+9 and 10k1+1, i.e. the last digits of the twin prime pairs are 9 and 1. The 9 ending is evident in this sequence. The table of the first 101 terms was computed using Zak Seidov's table.
LINKS
Cino Hilliard, List of n, a(n) for n=1..101
S. M. Ruiz, Integer then equal.
Sebastian Martin Ruiz and others, Integers then Equals, digest of 7 messages in primenumbers Yahoo group, Mar 14 - Mar 20, 2009.
Zak Seidov, A158470 first 101 terms.
FORMULA
Prime(n) is the n-th prime number.
EXAMPLE
For n = 11, prime(11-1)=29, 29+7=36; prime(11+1)=37, 37-1=36. So 29 is the first entry in the sequence.
MATHEMATICA
ppQ[{a_, b_}]:=Module[{s=Prime[a+1]-1}, IntegerQ[Sqrt[s]]&&b+7==s]; Select[ Table[ {n, Prime[n-1]}, {n, 2, 133*10^5}], ppQ][[All, 2]] (* Harvey P. Dale, Jul 31 2020 *)
PROG
(PARI) \\Copy and paste the Zak's file to zaklist.txt and edit to a straight
\\list with CR after each entry. Start a new Pari sesion then \r zakilist.txt
integerequal(a, b) =
{
local(x, p1, p2);
for(j=1, 101,
x=eval(concat("%", j)); p1=prime2(x-1);
if(issquare(p1+a),
p2=prime2(x+1); if((p1+a)==(p2-b),
print1(p1", ")
)
prime2(n) = \\the n-th prime using c:\sieve\prime.exe calling 8byte binary
\\g:\sievedata\prime2-1trill.bin" 300 gig file of primes <10^12
{
local(x, s);
s=concat("c:/sieve/prime ", Str(n));
s=concat(s, " > temp.txt");
\\Must save to a temp file for correct output
system(s);
return(read("temp.txt"))
}
)
)
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Mar 20 2009
EXTENSIONS
Edited by N. J. A. Sloane Aug 31 2009 (rephrased definition, corrected offset).
STATUS
approved