A213159 -id:A213159 - cp's OEIS frontend

A213161 Primes p such that (k+1)*p^2-k are prime for k=1..7.

1329433951, 25778112821, 75902670689, 80358496679, 84005465699, 184273377289, 188745495049, 220260667439, 225830918741, 227706130541, 250232659249, 314987199911, 396580371571, 532375084669, 535798256839, 542604984109, 634725913009, 676837365821, 706769028239

Offset: 1

Zak Seidov, Jun 06 2012

nonn

All terms squared are congruent to 1 mod 9240.
More terms: 755943098371, 797370889699, 843028736089, 848657766529, 849148113659, 861950855039, 1035653917759.
Subsequence of A213159: a(1)=A213159(8)=A213125(134).

Cf. A106483, A213078, A213079, A213107, A213125, A213159.

A213334 Primes p such that (k+1)*p^2 - k is prime for k=1..8.

Original entry on oeis.org

75902670689, 84005465699, 188745495049, 220260667439, 314987199911, 1970532645509, 2368000666921, 3702971171899, 3886185845431, 4117783215701, 4166366916251, 6213125459729, 7768065083591, 7946042954849, 8788172678669, 11387502711311, 14643617926211

Offset: 1

Zak Seidov, Jun 08 2012

The square of each term is congruent to 1 (mod 9240).

Note that for each p, (k+1)*p^2 - k (k=1..8) gives 8 primes in arithmetic progression with difference d = p^2 - 1.

Subsequence of A213161. Cf. A106483, A213078, A213079, A213107, A213125, A213159.

a(6)-a(17) from Tyler Busby, Jan 09 2023

A213162 Smallest prime p such that (k+1)*p^2-k are prime for k=1..n.

Original entry on oeis.org

2, 199, 409, 17569, 981091, 3918251, 1329433951, 75902670689, 45048280453021

Offset: 1

Zak Seidov, Jun 06 2012

a(1..8) are the first terms correspondingly in A106483, A213078, A213079, A213107, A213125, A213159, A213161, A213334.

a(n) = {my(p = 2); until (ok, ok = 1; for (k = 1, n, if (! isprime((k+1)*p^2-k), ok = 0; break;);); if (!ok, p = nextprime(p+1);)); return (p);}  \\ Michel Marcus, Apr 19 2013

a(9) from Tyler Busby, Jan 11 2023

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A213161 Primes p such that (k+1)*p^2-k are prime for k=1..7.

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A213334 Primes p such that (k+1)*p^2 - k is prime for k=1..8.

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A213162 Smallest prime p such that (k+1)*p^2-k are prime for k=1..n.

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