A091727 -id:A091727 - cp's OEIS frontend

A091728 Number of prime ideals of Z[sqrt(-5)] of norm n.

0, 1, 2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Paul Boddington, Feb 02 2004

It follows that the total number of ideals of norm n is A035170(n).

David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.
A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A035170, A091727.

isA091727(n) = { my(ms = [1, 2, 3, 5, 7, 9], p, e=isprimepower(n,&p)); if(!e || e>2, 0, bitxor(e-1,!!vecsearch(ms,p%20))); };
A091728(n) = if(!isA091727(n),0,(2-((2==n)||(5==n)||issquare(n)))); \\ Antti Karttunen, Feb 24 2020

a(n)=0 if n is not in A091727. If n is in A091727 and n is 2, 5 or a square then a(n)=1. Otherwise a(n)=2.

Data section extended up to a(121) by Antti Karttunen, Feb 24 2020

A225659 Primes p where p + sumOfDigits(p) +- 3 is prime.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 131, 137, 139, 157, 173, 179, 191, 197, 223, 227, 229, 241, 263, 269, 283, 311, 313, 317, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 463, 467, 487, 557

Offset: 1

John-Å. W. Olsen, May 11 2013

a(n) = A068690(n), A030144(n), A069556(n), A091727(n), A156756(n) if n<14.

			If p = 409, then 409 + sod(409) +- 3 = 409+13 - 3 = 419, which is prime.
If p =  23, then  23 + sod(23)  +- 3 = 23+5   + 3 = 31,  which is prime.

Andrew Howroyd, Table of n, a(n) for n = 1..394

Cf. A000040, A007605, A068690, A030144, A069556, A091727, A156756.

Select[Prime[Range[102]],Or@@PrimeQ[#+Total[IntegerDigits[#]]+{3,-3}] &] (* Jayanta Basu, May 23 2013 *)

ok(p)= {my(s=vecsum(digits(p)));isprime(p) && (isprime(p+s-3) || isprime(p+s+3))}
select(ok,[1..1000]) \\ Andrew Howroyd, Feb 22 2018

cp's OEIS Frontend

A091728 Number of prime ideals of Z[sqrt(-5)] of norm n.

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