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
a(2)=971: 10^3-prime(10)= 1000-29= 971 which is prime.
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KD:= proc() local a; a:= k^3-ithprime(k); if isprime(a) then RETURN(a): fi; end: seq(KD(),k=1..1000);
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Select[Table[k^3-Prime[k],{k,1000}],PrimeQ]
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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
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.
Cf.
A184935 (primes: k^2 + prime(k)).
Cf.
A188831 (primes: k^2 - prime(k)).
Cf.
A229203 (primes: k^3 - prime(k)).
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with(numtheory):KD := proc() local a; a:= (ithprime(k)^2+k); if isprime(a) then RETURN (a); fi; end: seq(KD(),k=1..1000);
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Select[Table[Prime[k]^2 + k, {k, 1000}], PrimeQ]
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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
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.
Cf.
A184935 (primes: k^2 + prime(k)).
Cf.
A188831 (primes: k^2 - prime(k)).
Cf.
A229203 (primes: k^3 - prime(k)).
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with(numtheory):KD := proc() local a; a:= (ithprime(k)^2-k); if isprime(a) then RETURN (a); fi; end: seq(KD(), k=1..1000);
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Select[Table[Prime[k]^2-k,{k,1000}],PrimeQ]
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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
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.
Cf.
A184935 (primes: k^2 + prime(k)).
Cf.
A188831 (primes: k^2 - prime(k)).
Cf.
A229203 (primes: k^3 - prime(k)).
Cf.
A212304 (primes: prime(k)^2 + k).
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[q: k in [1..1000] | IsPrime(q) where q is NthPrime(k)^3+k]; // Bruno Berselli, Mar 26 2014
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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);
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Select[Table[Prime[k]^3 + k, {k, 1000}], PrimeQ]
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s=[]; for(k=1, 1000, n=prime(k)^3+k; if(isprime(n), s=concat(s, n))); s \\ Colin Barker, Mar 26 2014
Showing 1-4 of 4 results.