A089782 -id:A089782 - cp's OEIS frontend

A089783 Smallest prime(k) pertaining to A089782.

2, 3, 3, 2, 3, 5, 37, 2, 2, 3, 11, 2, 3, 3, 3, 17, 3, 47, 2, 3, 3, 2, 3, 53, 5, 17, 3, 41, 2, 11, 2, 2, 29, 19, 11, 3, 3, 5, 19, 2, 3, 5, 7, 13, 17, 5, 11, 3, 11, 11, 2, 3, 2, 29, 17, 2, 5, 211, 2, 83, 2, 13, 2, 31, 3, 5, 3, 2, 17, 3, 11, 3, 41, 17, 2, 2, 167, 5, 17, 5, 11, 3, 5, 5, 3, 3, 3, 3, 3

Offset: 1

Amarnath Murthy, Nov 24 2003

			a(4) = 2 as 2= prime(1) followed by prime(1+4) is prime.

Cf. A089782.

More terms from David Wasserman, Oct 13 2005

A089785 a(n) is the least prime(k) such that the concatenation of prime(k) and prime(k-n) is prime.

Original entry on oeis.org

5, 7, 11, 19, 17, 19, 23, 29, 31, 37, 67, 43, 83, 61, 59, 61, 67, 79, 73, 113, 97, 167, 107, 101, 103, 149, 109, 137, 167, 163, 137, 179, 149, 163, 257, 179, 277, 173, 251, 199, 191, 193, 197, 199, 211, 229, 227, 229, 233, 239, 281, 347, 283, 263, 269, 271, 283

Offset: 1

Amarnath Murthy, Nov 24 2003

			a(4) = 19 =prime(8) and prime(8) followed by prime(8-4) =197 is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A089782, A089783.

f:= proc(n) local p,k,q,d;
 p:= ithprime(n);
 for k from n+1 do
   p:= nextprime(p);
   q:= ithprime(k-n);
   d:= ilog10(q)+1;
   if isprime(p*10^d+q) then return p fi
 od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 13 2017

More terms from David Wasserman, Oct 13 2005

A089786 Primes of the form prime(2k) followed by prime(k).

Original entry on oeis.org

73, 197, 7129, 10141, 15161, 19379, 271109, 373157, 593251, 757331, 983431, 997433, 1069463, 1231547, 1361599, 1531661, 1571683, 1627727, 1831811, 2069911, 2161967, 2213977, 24731093, 25311103, 26931193, 27131213, 27911237, 28191259

Offset: 1

Amarnath Murthy, Nov 24 2003

			10141 is a term as a concatenation of prime(26)=101 followed by prime(13)=41.

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

Cf. A089782, A089783, A089784, A089785, A089787.

a:=proc(k) local s,m: s:= [op(convert(ithprime(k),base,10)),op(convert(ithprime(2*k),base,10))]: m:=add(s[j]*10^(j-1),j=1..nops(s)): if not isprime(m) then RETURN(NULL) else RETURN(m) fi: end; seq(a(k),k=1..250); (C. Ronaldo)

Select[Table[FromDigits[Flatten[IntegerDigits/@{Prime[2n],Prime[n]}]],{n,250}],PrimeQ] (* Harvey P. Dale, Nov 17 2014 *)

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004

A089788 Primes of the form prime(nk) followed by prime(k).

Original entry on oeis.org

73, 6113, 193, 293, 373, 433, 26317, 613, 94153, 38917, 2237, 1013, 43313, 76123, 82723, 76919, 70117, 169943, 1733, 4337, 1933, 1993, 421189, 2293, 2393, 195131, 2633, 2713, 86311, 510179, 94111, 97711, 3373, 129113, 3593, 3733, 3833, 268729

Offset: 1

Amarnath Murthy, Nov 24 2003

Cf. A089782, A089783, A089784, A089785, A089786, A089787, A089789.

c[r_, s_] := ToExpression[ToString[r] <> ToString[s]]; Do[k = 1; While[ !PrimeQ[c[Prime[n*k], Prime[k]]], k++ ]; Print[c[Prime[n*k], Prime[k]]], {n, 2, 100}] (* Ryan Propper, Sep 14 2005 *)

More terms from Ryan Propper, Sep 14 2005

cp's OEIS Frontend

A089783 Smallest prime(k) pertaining to A089782.

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A089785 a(n) is the least prime(k) such that the concatenation of prime(k) and prime(k-n) is prime.

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A089786 Primes of the form prime(2k) followed by prime(k).

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Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A089788 Primes of the form prime(nk) followed by prime(k).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Extensions