A229289 Primes p of the form p = 2^k * m + 1, where (i) m is squarefree and odd, (ii) all primes that divide m are in the sequence, and (iii) k is 0, 1, or 2.
2, 3, 5, 7, 11, 13, 23, 29, 31, 43, 47, 53, 59, 61, 67, 71, 79, 107, 131, 139, 157, 173, 211, 263, 269, 277, 283, 311, 317, 331, 347, 349, 367, 373, 421, 431, 461, 463, 547, 557, 599, 643, 659, 661, 683, 691, 709, 733, 743, 787, 827, 853, 859, 863, 911, 941
Offset: 1
Keywords
Links
- Ray Chandler, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Mathematica
fa = FactorInteger; free[n_] := n == Product[fa[n][[i, 1]], {i, Length[fa[n]]}] ; Os[b_, 1] = True; Os[b_, b_] = True; Os[b_, n_] := Os[b, n] = PrimeQ[n] && free[(n - 1)/b^IntegerExponent[n - 1, b]] &&IntegerExponent[n - 1, b] < 3 && Union@Table[Os[b, fa[n - 1][[i, 1]]], {i, Length[fa[n - 1]]}] == {True};G[b_] := Select[Prime[Range[1000]], Os[b, #] &];G[2] -
PARI
is(n)=if(!isprime(n),return(0)); if(n<13,return(1)); my(k=valuation(n-1,2), m=n>>k, f); if(k>2,return(0)); f=factor(m); if(lcm(f[,2])>1, return(0)); for(i=1,#f~, if(!is(f[i,1]), return(0))); 1 \\ Charles R Greathouse IV, Oct 28 2013
Extensions
Revised definition from Charles R Greathouse IV, Nov 13 2013
Terms corrected by José María Grau Ribas, Nov 14 2013
Comments