A184935 -id:A184935 - cp's OEIS frontend

A064711 Numbers n such that n^2 + prime(n) is a prime.

1, 2, 4, 8, 12, 14, 22, 30, 36, 38, 44, 50, 54, 60, 66, 74, 78, 84, 90, 96, 106, 134, 144, 156, 162, 168, 180, 188, 216, 222, 224, 234, 260, 264, 272, 308, 324, 336, 344, 366, 368, 374, 378, 390, 402, 406, 422, 466, 468, 476, 492, 498, 502, 516, 604, 624, 636

Offset: 1

Robert G. Wilson v, Oct 13 2001

			2 is in the sequence because 2^2 + Prime(2) = 4 + 3 = 7 is a prime.

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

Cf. A004232, A184935.

[ n: n in [1..700] | IsPrime(n^2+NthPrime(n)) ]; // Klaus Brockhaus, Apr 12 2011

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

{ n=0; for (m=1, 10^9, if (isprime(m^2 + prime(m)), write("b064711.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)).

A004232 a(n) = n^2 + prime(n).

Original entry on oeis.org

3, 7, 14, 23, 36, 49, 66, 83, 104, 129, 152, 181, 210, 239, 272, 309, 348, 385, 428, 471, 514, 563, 612, 665, 722, 777, 832, 891, 950, 1013, 1088, 1155, 1226, 1295, 1374, 1447, 1526, 1607, 1688, 1773, 1860, 1945, 2040, 2129, 2222, 2315, 2420, 2527, 2628, 2729

Offset: 1

wild(AT)edumath.u-strasbg.fr (Daniel Wild)

Sum of reciprocals = 0.766167481.... - Cino Hilliard, Dec 31 2003
The subset of primes begins: 3, 7, 23, 83, 181, 239, 563, 1013, 1447, 1607, 2129, 2729 = A184935. The subset of squares begins: 36, 49, no more through n = 100. - Jonathan Vos Post, Feb 02 2011
No more squares using primes < 10^10 (n ~ 45 million). The naive heuristic (not really applicable here, but it's a starting point) suggests something like sqrt(log(x)) up to x. - Charles R Greathouse IV, Feb 06 2011

Cf. A184935.

[n^2 +NthPrime(n): n in [1..250]]; // Vincenzo Librandi, Apr 14 2011

Table[n^2+Prime[n],{n,50}] (* Harvey P. Dale, Feb 28 2015 *)

primeppwr(n) = sr=0; for(x=1,n, y=x^2+prime(x); print1(y","); sr+=1./y; ); print(); print(sr) \\ Cino Hilliard

More terms from Cino Hilliard, Dec 31 2003

A229203 Primes of the form k^3 - prime(k).

Original entry on oeis.org

5, 971, 54709, 73907, 84991, 124771, 287179, 404851, 511591, 728537, 4095059, 5638691, 6433747, 6857849, 10646627, 11238001, 11850913, 12811423, 13479779, 13822489, 14170957, 16775597, 17574343, 19681267, 20121901, 21950189, 26461619, 39999391, 49025423, 49833529

Offset: 1

K. D. Bajpai, Sep 15 2013

nonn

			a(2)=971: 10^3-prime(10)= 1000-29= 971 which is prime.

K. D. Bajpai, Table of n, a(n) for n = 1..5500

Cf. A188831, A184935.

KD:= proc() local a; a:= k^3-ithprime(k); if isprime(a) then RETURN(a): fi; end: seq(KD(),k=1..1000);

Select[Table[k^3-Prime[k],{k,1000}],PrimeQ]

for(k=1, 10^3, if(ispseudoprime(KD=eval((k^3-prime(k)))), print1(KD", ")));

A212304 Primes of the form prime(n)^2 + n.

Original entry on oeis.org

5, 11, 53, 1381, 3739, 6263, 12799, 32803, 57173, 177323, 187573, 491527, 674183, 1067263, 1125899, 1142941, 1230067, 1352761, 1471567, 1745257, 1885349, 2283361, 2563453, 2779151, 3893027, 4364237, 5508757, 6933071, 7513481, 7790087, 8048981, 9370159, 11499359

Offset: 1

K. D. Bajpai, Oct 24 2013

nonn

			a(3) = 53 :  prime(4)^2 + 4 = 7^2 + 4 = 49 + 4 = 53 which is prime.
a(4) = 1381 :  prime(12)^2 + 12 = 37^2 + 12 = 1369 + 12 = 1381 which is prime.

K. D. Bajpai, Table of n, a(n) for n = 1..6700

Cf. A000040 (prime numbers).
Cf. A184935 (primes: k^2 + prime(k)).
Cf. A188831 (primes: k^2 - prime(k)).
Cf. A229203 (primes: k^3 - prime(k)).

with(numtheory):KD := proc() local a; a:= (ithprime(k)^2+k); if isprime(a) then RETURN (a); fi; end: seq(KD(),k=1..1000);

Select[Table[Prime[k]^2 + k, {k, 1000}], PrimeQ]

for(k=1, 10^5, if(ispseudoprime(KD=((prime(k)^2+k))), print1(KD", ")));

A227890 Primes of the form prime(k)^2 - k.

Original entry on oeis.org

3, 7, 163, 353, 5021, 12739, 32719, 49681, 52391, 78901, 113501, 252913, 361091, 452807, 551917, 993841, 1559797, 1956979, 2193127, 3463037, 4067983, 5003837, 5138953, 6115363, 6723271, 7251857, 7447043, 7578607, 8426989, 9479801, 11295847, 12186593, 12439237

Offset: 1

K. D. Bajpai, Oct 26 2013

nonn

			a(3)= 163: prime(6)^2 - 6= 13^2 - 6= 169 - 6= 163 which is prime.
a(4)= 353: prime(8)^2 - 8= 19^2 - 8= 361 - 8= 353 which is prime.

K. D. Bajpai, Table of n, a(n) for n = 1..7200

Cf. A000040 (prime numbers).
Cf. A064713 (for the integers k).
Cf. A184935 (primes: k^2 + prime(k)).
Cf. A188831 (primes: k^2 - prime(k)).
Cf. A229203 (primes: k^3 - prime(k)).

with(numtheory):KD := proc() local a; a:= (ithprime(k)^2-k); if isprime(a) then RETURN (a); fi; end: seq(KD(), k=1..1000);

Select[Table[Prime[k]^2-k,{k,1000}],PrimeQ]

for(k=1, 10^5, if(ispseudoprime(KD=((prime(k)^2-k))), print1(KD", ")));

A239743 Primes of the form prime(k)^3 + k.

Original entry on oeis.org

29, 347, 2203, 704993, 2248123, 2685653, 3442987, 81182821, 86938393, 95444081, 230346509, 1064332433, 1298596753, 1829276767, 2202074113, 3449796071, 4306879141, 6740558659, 8205739219, 9649993009, 11650768499, 14225261327, 15124198183, 19968681493, 21415471837

Offset: 1

K. D. Bajpai, Mar 26 2014

nonn

			29 is in the sequence because prime(2)^3 + 2 = 29, which is prime.
347 is in the sequence because prime(4)^3 + 4 = 347, which is prime.

K. D. Bajpai, Table of n, a(n) for n = 1..7000

Cf. A000040 (prime numbers).
Cf. A184935 (primes: k^2 + prime(k)).
Cf. A188831 (primes: k^2 - prime(k)).
Cf. A229203 (primes: k^3 - prime(k)).
Cf. A061068 (primes: prime(k) + k)
Cf. A212304 (primes: prime(k)^2 + k).

[q: k in [1..1000] | IsPrime(q) where q is NthPrime(k)^3+k]; // Bruno Berselli, Mar 26 2014

KD := proc() local a,b; a:= ithprime(n); b:=a^3+n; if isprime(b) then RETURN (b); fi; end: seq(KD(), n=1..1000);

Select[Table[Prime[k]^3 + k, {k, 1000}], PrimeQ]

s=[]; for(k=1, 1000, n=prime(k)^3+k; if(isprime(n), s=concat(s, n))); s \\ Colin Barker, Mar 26 2014

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A064711 Numbers n such that n^2 + prime(n) is a prime.

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

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A004232 a(n) = n^2 + prime(n).

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A229203 Primes of the form k^3 - prime(k).

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A212304 Primes of the form prime(n)^2 + n.

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A227890 Primes of the form prime(k)^2 - k.

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A239743 Primes of the form prime(k)^3 + k.

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