A335410 -id:A335410 - cp's OEIS frontend

A335778 The square roots of the perfect squares produced by A335410 in the order in which they appear.

12, 12, 24, 36, 60, 84, 84, 132, 96, 372, 144, 408, 168, 180, 732, 468, 348, 1032, 408, 1392, 528, 1704, 612, 1956, 948, 744, 2316, 1092, 816, 1212, 1236, 2724, 912, 2616, 2820, 948, 1092, 1548, 1188, 1200, 1716

Offset: 1

Jeff Brown, Jun 22 2020

nonn

			11 is in sequence A335410.  2*(11^2 - 7^2) = 144 = 12^2.  Therefore, 12 is in this sequence.

Cf. A335410.

Select[IntegerQ][Table[Sqrt[2*Prime[n]^2 - 2*Prime[n-1]^2], {n,17000}]]

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

A332615 Primes prime(k) such that 2*(prime(k)^2 - prime(k-1)^2) is a fourth power.

Original entry on oeis.org

83, 2593, 194483, 388963, 31505923, 57289763, 96059603, 99574273, 169869313, 276922883, 395254163, 414720001, 3264481603, 5125781251, 6059221283, 18233242723, 35888419873, 82012500001, 135304020001, 154550410643, 159004011043, 186320859203, 206710354243, 364488705443

Offset: 1

Jeff Brown, Jun 08 2020

nonn

This is a subset of A335410.

			Prime(23)=83. Prime(22)=79. 2*(83^2 - 79^2) = 6^4.
Prime(378)=2593. Prime(377)=2591. 2*(2593^2 - 2591^2) = 12^4.

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 102 terms from Chai Wah Wu)

Cf. A001248, A335410.

Select[Prime@Range[2, 500000], IntegerQ@Sqrt[Sqrt[2(#^2 - NextPrime[#, -1]^2)]]&] (* a modification of Giovanni Resta's program for A335410 *)

isok(p) = isprime(p) && ispower(2*(p^2-precprime(p-1)^2), 4); \\ Michel Marcus, Jun 08 2020

lista(nn) = {my(pp=2); forprime(p=3, nn, if (ispower(2*(p^2 - pp^2), 4), print1(p, ", ")); pp = p;);} \\ Michel Marcus, Jun 08 2020

More terms from Amiram Eldar, Jun 08 2020

More terms from Giovanni Resta, Jun 08 2020

A332333 a(n) = A335778(n)/12.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 7, 11, 8, 31, 12, 34, 14, 15, 61, 39, 29, 86, 34, 116, 44, 142, 51, 163, 79, 62, 193, 91, 68, 101, 103, 227, 76, 218, 235, 79, 91, 129, 99, 100, 143, 147, 149, 107, 310, 473, 343, 171, 125, 394, 187, 401, 191, 142, 203, 147, 418, 460, 156

Offset: 1

Jeff Brown, Jul 06 2020

nonn

Cf. A335410, A335778.

Select[IntegerQ][Table[Sqrt[2*Prime[n]^2 - 2*Prime[n-1]^2]/12, {n, 37000}]]

cp's OEIS Frontend

A335778 The square roots of the perfect squares produced by A335410 in the order in which they appear.

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A332615 Primes prime(k) such that 2*(prime(k)^2 - prime(k-1)^2) is a fourth power.

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A332333 a(n) = A335778(n)/12.

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