A332615 -id:A332615 - cp's OEIS frontend

A335410 Primes prime(k) such that 2*(prime(k)^2 - prime(k-1)^2) is a perfect square.

11, 19, 73, 83, 227, 443, 883, 1091, 1153, 1931, 2593, 2609, 3529, 4051, 7451, 13691, 15139, 16649, 20809, 26921, 34849, 45377, 46819, 53147, 56171, 69193, 74507, 74531, 83233, 91811, 95483, 103067, 103969, 106937, 110459, 112339, 149059, 149771, 176419, 180001

Offset: 1

Jeff Brown, Jun 06 2020

nonn

2*(prime(n)^2 - prime(n-1)^2) represents the integer coefficient of the difference in areas between the two circles passing through the origin with centers located at (prime(n), prime(n)) and (prime(n-1), prime(n-1)).

Among the first 200000 primes 2593 and 2609 are the only consecutive primes in this sequence.

			Prime(5) = 11, prime(4) = 7, 2*(11^2 - 7^2) = 12^2, so 11 is in the sequence.
Prime(559) = 4051, prime(558) = 4049, 2*(4051^2 - 4049^2) = 180^2, so 4051 is in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001248, A332615.

Select[Prime@ Range[2, 17000], IntegerQ@ Sqrt[2 (#^2 - NextPrime[#, -1]^2)] &] (* Giovanni Resta, Jun 06 2020 *)

lista(nn) = {my(pp=2); forprime (p=3, nn, if (issquare(2*(p^2 - pp^2)), print1(p, ", ")); pp = p;);} \\ Michel Marcus, Jun 25 2020

More terms from Giovanni Resta, Jun 06 2020

cp's OEIS Frontend

A335410 Primes prime(k) such that 2*(prime(k)^2 - prime(k-1)^2) is a perfect square.

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