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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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Taking m=1 in the definition we get the primes 2, 3, 5.

If n is in A226960, then n is a product of terms of this sequence.

If k is only allowed to be 0 or 1, we get 2, 3, 7, 43 and no more. - Jianing Song, Feb 21 2021

Also prime factors of terms in A341858. It is conjectured that this sequence is infinite. - Jianing Song, Feb 22 2021

LINKS

Ray Chandler, Table of n, a(n) for n = 1..1000

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]

PROG

(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

CROSSREFS

Cf. A227007, A226960, A007814, A229290, A229291, A289355, A341858.

For the complement, see A289355.

Proper subsequence of A066651.

Sequence in context: A181172 A075430 A095080 * A087634 A291691 A178576

Adjacent sequences:  A229286 A229287 A229288 * A229290 A229291 A229292

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Oct 05 2013

EXTENSIONS

Revised definition from Charles R Greathouse IV, Nov 13 2013

Terms corrected by José María Grau Ribas, Nov 14 2013

STATUS

approved

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Last modified May 13 05:02 EDT 2021. Contains 343836 sequences. (Running on oeis4.)