A073497 -id:A073497 - cp's OEIS frontend

A064712 Numbers k such that k^2 - prime(k) is a prime.

6, 10, 12, 18, 24, 28, 30, 40, 42, 48, 60, 76, 96, 104, 108, 114, 138, 146, 160, 166, 174, 176, 186, 190, 196, 198, 208, 230, 250, 258, 262, 270, 292, 296, 318, 320, 334, 336, 348, 356, 358, 362, 370, 372, 376, 382, 400, 420, 444, 454, 462, 472, 488, 494, 504

Offset: 1

Robert G. Wilson v, Oct 13 2001

A073497(a(n)) is a prime. - Zak Seidov, Apr 11 2011

			6 is in the sequence because 6^2 - prime(6) = 36 - 13 = 23 is a prime.

Harry J. Smith, Table of n, a(n) for n = 1..1000

[n: n in [6..1000] | IsPrime(n^2-NthPrime(n))]; // Vincenzo Librandi, Apr 14 2011

Select[ Range[ 6,1000,2 ], PrimeQ[ #^2 - Prime[ # ] ] & ]

n=0; forstep (m=6, 10^9, 2, if (isprime(m^2 - prime(m)), write("b064712.txt", n++, " ", m); if (n==1000, break)) ) \\ Harry J. Smith, Sep 23 2009

A188831 Primes of the form k^2 - prime(k).

Original entry on oeis.org

23, 71, 107, 263, 487, 677, 787, 1427, 1583, 2081, 3319, 5393, 8713, 10247, 11071, 12377, 18257, 20477, 24659, 26573, 29243, 29927, 33487, 34949, 37223, 37991, 41981, 51449, 60917, 64937, 66977, 71167, 83357, 85667, 99013, 100271, 109313, 110629, 118757

Offset: 1

Zak Seidov, Apr 11 2011

nonn

Or, primes in A073497. Corresponding values of k in A064712.
This is to A073497 and A064712 as A184935 is to A004232 and A064711.
The two primes prime(k) and k^2-prime(k) are a Goldbach partition of k^2. - T. D. Noe, Apr 14 2011

			23 is here because 6^2 - prime(6) = 36 - 13 = 23.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A004232, A064711, A064712, A073497, A184935.

[ a: k in [0..10000] | IsPrime(a) where a is k^2-NthPrime(k) ]; // Vincenzo Librandi, Apr 14 2011

Select[Table[k^2 - Prime[k], {k, 1000}], PrimeQ] (* T. D. Noe, Apr 14 2011 *)

a(n) = A073497(A064712(n)).

A108753 Difference between the n-th partial sum of the squares (A000330) and the n-th partial sum of the primes (A007504).

Original entry on oeis.org

-1, 0, 4, 13, 27, 50, 82, 127, 185, 256, 346, 453, 581, 734, 912, 1115, 1345, 1608, 1902, 2231, 2599, 3004, 3450, 3937, 4465, 5040, 5666, 6343, 7075, 7862, 8696, 9589, 10541, 11558, 12634, 13779, 14991, 16272, 17626, 19053, 20555, 22138, 23796, 25539, 27367

Offset: 1

Alexandre Wajnberg, Jun 23 2005

Numbers congruent to {0, 3, 8, 11} mod 12.

			a(4) = A000330(4) - A007504(4) = (1 + 4 + 9 + 16) - (2 + 3 + 5 + 7) = 30 - 17 = 13.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000330, A007504.

Partial sums of A073497.

f[n_] := n(n + 1)(2n + 1)/6 - Sum[Prime[i], {i, n}]; Table[ f[n], {n, 15}] (* Robert G. Wilson v, Jun 25 2005 *)
#[[1]]-#[[2]]&/@With[{nn=50},Thread[{Accumulate[Range[nn]^2], Accumulate[ Prime[ Range[nn]]]}]] (* Harvey P. Dale, May 07 2013 *)

Edited and extended by Robert G. Wilson v, Jun 25 2005

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A064712 Numbers k such that k^2 - prime(k) is a prime.

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A188831 Primes of the form k^2 - prime(k).

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A108753 Difference between the n-th partial sum of the squares (A000330) and the n-th partial sum of the primes (A007504).

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