A156152
Primes p such that p = 2 (mod pi(p)), where pi(p) = A000720(p) is the prime counting function.
Original entry on oeis.org
2, 5, 41, 47, 347, 367, 9559817, 514272793, 514274807, 514275529, 3779851091, 27788568469, 27788573621, 204475055227, 11091501631937, 81744303098923, 602656752070661, 602656752071189, 241849345578327359, 241849345578328451, 241849345578337811, 1784546064357416683
Offset: 1
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f[p_,n_]:=Mod[p,n]==2; lst={};Do[p=Prime[n];If[f[p,n],AppendTo[lst,p]],{n,11!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 08 2009 *)
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p=c=0; until(0, (-2+p=nextprime(p+1))%c++ || print1(p, ", "))
A156154
Primes p such that prime(p)=2 (mod p), where prime(p)=A000040(p) is the p-th prime.
Original entry on oeis.org
3, 13, 73, 637321, 27067133
Offset: 1
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Select[Prime[Range[17*10^5]],Mod[Prime[#],#]==2&] (* Harvey P. Dale, Dec 28 2022 *)
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p=c=0; until(0, until( isprime(c++), p=nextprime(p+1)); (p-2)%c & next; print1( c","))
A156150
Primes p such that p+2 = 0 (mod pi(p)) and pi(p)=A000720(p) is prime.
Original entry on oeis.org
31, 353, 9559783, 9559903
Offset: 1
A328022
Prime numbers p such that all 4 variables of the equation (p = i * q + r) are prime, with i being the index of p, q the quotient of p/i, and r the remainder of p/i.
Original entry on oeis.org
17, 41, 367, 514275529
Offset: 1
Known values:
n | a(n) = p = i * q + r
===+==============================
1 | 17 = 7 * 2 + 3
2 | 41 = 13 * 3 + 2
3 | 367 = 73 * 5 + 2
4 | 514275529 = 27067133 * 19 + 2
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Select[Prime@ Range[10^5], AllTrue[Join[{#1, #2}, QuotientRemainder[#1, #2]], PrimeQ] & @@ {#, PrimePi@ #} &] (* Michael De Vlieger, Oct 01 2019 *)
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lista(nn)={my(i=1); forprime(p=3, nn, i++; if(isprime(i), my(q=p\i); if(isprime(q)&&isprime(p-q*i), print1(p, ", ")) ))} \\ Andrew Howroyd, Oct 01 2019
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