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A173415 Numbers n such that both the difference and the sum of (n-th prime+1)^2 and (n-th prime)^2 are prime. 0
1, 3, 10, 128, 201, 223, 246, 309, 357, 393, 424, 482, 526, 815, 887, 909, 1014, 1196, 1543, 1610, 1653, 1674, 1743, 2219, 2302, 2339, 2371, 2475, 2513, 2611, 2948, 3107, 3273, 3419, 3434, 3516, 3555, 3593, 4070, 4203, 4288, 4332, 4389, 4428, 4724, 4793 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..46.

FORMULA

a(n) = Pi(A098717(n)) = A049084(A098717(n)). - R. J. Mathar, Mar 09 2010

EXAMPLE

a(1)=1 because (1st prime+1)^2 - (1st prime)^2=5 is prime and (1st prime+1)^2 + (1st prime)^2=13 is prime;

a(2)=3 because (3rd prime+1)^2 - (3rd prime)^2=11 is prime and (3rd prime+1)^2 + (3rd prime)^2=61 is prime;

a(3)=10 because (10th prime+1)^2 - (10th prime)^2=59 is prime and (10th prime+1)^2 + (10th prime)^2=1741 is prime;

a(4)=128 because (128th prime+1)^2 - (128th prime)^2=1439 is prime and (128th prime+1)^2 + (128th prime)^2=1035361 is prime.

MATHEMATICA

npsQ[n_]:=Module[{np=Prime[n], a, b}, a=np^2; b=(np+1)^2; And@@PrimeQ[ {a+b, b-a}]]; Select[Range[5000], npsQ] (* Harvey P. Dale, Sep 11 2011 *)

CROSSREFS

Cf. A000040, A068501.

Sequence in context: A290059 A062006 A199036 * A199232 A056006 A191363

Adjacent sequences:  A173412 A173413 A173414 * A173416 A173417 A173418

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Mar 01 2010

EXTENSIONS

Extended beyond a(4) by R. J. Mathar, Mar 09 2010

STATUS

approved

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Last modified April 3 22:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)