A242489 Smallest even k such that lpf(k-1) = prime(n), while lpf(k-3) > prime(n), where lpf=least prime factor (A020639).

10, 26, 50, 254, 170, 392, 362, 944, 842, 1892, 1370, 2420, 1850, 2210, 3764, 6314, 3722, 4892, 5042, 7082, 8612, 9380, 7922, 12320, 11414, 10610, 11450, 13844, 18872, 16130, 17162, 20414, 19322, 26672, 24614, 25592, 29504, 37910, 29930, 44930, 36020, 36482

Offset

2,1

Comments

This sequence is connected with a sufficient condition for the infinitude of twin primes.

Almost all numbers of the form a(n)-3 are primes. For composite numbers of such a form, see A242716.

Primes p for which a(p) = p^2+1 form sequence A062326 for p >= 3. - Vladimir Shevelev, May 21 2014

Links

Peter J. C. Moses, Table of n, a(n) for n = 2..2501

Formula

a(n) >= prime(n)^2+1. - Vladimir Shevelev, May 21 2014

Example

Let n=2, prime(2)=3. Then lpf(10-1)=3, but lpf(10-3)=7>3.
Since k=10 is the smallest such k, then a(2)=10.

Mathematica

lpf[n_]:=lpf[n]=First[Select[Divisors[n], PrimeQ[#]&]];
Table[test=Prime[n]; NestWhile[#+2&, test^2+1, !((lpf[#-1]==test)&&(lpf[#-3]>test))&], {n, 2, 60}] (* Peter J. C. Moses, May 21 2014 *)

Prog

(PARI) a(n) = {k = 6; p = prime(n); while ((factor(k-1)[1, 1] != p) || (factor(k-3)[1, 1] <= p), k+= 2); k; } \\ Michel Marcus, May 16 2014

Crossrefs

Cf. A001359, A006512.

Sequence in context: A134406 A099978 A242719 * A074789 A229308 A125075

Adjacent sequences: A242486 A242487 A242488 * A242490 A242491 A242492

Keyword

nonn

Author

Vladimir Shevelev, May 16 2014

Extensions

More terms from Michel Marcus, May 16 2014

Status

approved