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.

A192361 Primes p such that number of primes in the range (p-sqrt(p), p] is equal to number of primes in the range (p, p+sqrt(p)].

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%I A192361 #13 Jan 31 2024 13:37:58
%S A192361 2,11,29,37,41,71,97,103,131,191,229,257,263,311,331,347,373,379,443,
%T A192361 491,541,593,643,727,733,739,797,821,929,967,991,1013,1019,1097,1163,
%U A192361 1171,1201,1213,1217,1259,1291,1297,1373,1451,1481,1531,1553,1571,1583,1657,1709,1777,1831,1873,1949,1999,2053
%N A192361 Primes p such that number of primes in the range (p-sqrt(p), p] is equal to number of primes in the range (p, p+sqrt(p)].
%H A192361 Harvey P. Dale, <a href="/A192361/b192361.txt">Table of n, a(n) for n = 1..1000</a>
%e A192361 a(1)=2 because 2 in range (2-sqrt(2), 2] and 3 in range (2, 2+sqrt(2)],
%e A192361 a(2)=11 because 7 in range (11-sqrt(11), 11] and 13 in range (11, 11+sqrt(11)].
%t A192361 npeQ[p_]:=Module[{p1=PrimePi[p],p2=PrimePi[p-Sqrt[p]],p3=PrimePi[p+Sqrt[p]]},p3-p1 == p1-p2]; Select[Prime[Range[400]],npeQ] (* _Harvey P. Dale_, Jan 31 2024 *)
%o A192361 (PARI) is(p)=2*primepi(p)==primepi(p+sqrt(p))+primepi(p-sqrt(p))
%o A192361 select(isA192361,primes(1000)) \\ _Charles R Greathouse IV_, Jun 29 2011
%Y A192361 Cf. A058188.
%K A192361 nonn
%O A192361 1,1
%A A192361 _Juri-Stepan Gerasimov_, Jun 28 2011
%E A192361 Missing terms a(3) and a(7) inserted, a(19)-a(57) added by _Charles R Greathouse IV_, Jun 29 2011