A051919 -id:A051919 - cp's OEIS frontend

A051918 Start with n, apply k->2k+1 until reach new record prime; sequence gives number of steps needed.

2, 2, 2, 3, 4, 5, 5, 10, 13, 13, 26, 32, 287, 18380, 21727, 23205, 24828, 35646, 48819, 51476

Offset: 0

N. J. A. Sloane, Dec 18 1999

a(20) > 60000. [From Donovan Johnson, May 23 2010]

			0->1->3, new record prime 3 in 2 steps; 1->3->7, new record prime 7 in 2 steps; 2->5->11, new record prime 11 in 2 steps; 3->7->15->31, new record prime 31 in 3 steps.
For the next few terms we have: 4->9->19->39->79; 5->11->23->47->95->191; 6->13->27->55->111->223; 7->15->31->63->127->255->511->1023->2047->4095->8191; etc.

Cf. A051919, A052333.

f[0] = {start=0, k=3, steps=2}; f[n_] := f[n] = (k=start=f[n-1][[1]]+1; steps=0; While[!PrimeQ[k] || k <= f[n-1][[2]], k=2k+1; steps++]; {start, k, steps}); A051918 = Table[Print[f[n] // Last]; f[n], {n, 0, 13}][[All, 3]] (* Jean-François Alcover, Dec 10 2014 *)

More terms from Naohiro Nomoto, May 21 2001

a(13)-a(19) from Donovan Johnson, May 23 2010

A189657 Start with n, apply k->2k+1 until a semiprime is reached; sequence gives the semiprimes.

Original entry on oeis.org

15, 95, 15, 9, 95, 55, 15, 35, 39, 21, 95, 25, 55, 119, 511, 33, 35, 303, 39, 335, 87, 91, 95, 49, 51, 215, 55, 57, 119, 123, 511, 65, 543, 69, 143, 295, 303, 77, 159, 327, 335, 85, 87, 5759, 91, 93, 95, 391, 799, 203, 415, 54271, 215, 219, 111, 3647, 115

Offset: 0

Jonathan Vos Post, Apr 25 2011

This is to semiprimes A001358 as A051919 is to primes A000040. Is this sequence defined for all n?

			a(0) = 15 in 4 steps because 2*(2*(2*((2*0)+1)+1)+1)+1 = 15 = 3*5 is semiprime.
a(1) = 15 in 3 steps because 2*(2*((2*1) + 1)+1)+1 = 15 = 3*5
a(2) = 95 in 5 steps because 2*(2*(2*(2*(2*2 + 1)+1)+1)+1)+1 = 95 = 5*19.

Cf. A001358, A051919.

semiPrimeQ[n_] := Total[FactorInteger[n]][[2]]==2; Table[k = n; While[k = 2 k + 1; ! semiPrimeQ[k]]; k, {n, 100}] (* T. D. Noe, Apr 29 2011 *)

Extended by T. D. Noe, Apr 29 2011

A287766 Numbers k such that (10^k*113 + 19)/3 is prime.

Original entry on oeis.org

1, 9, 13, 33, 81, 1113, 1609, 5697, 13577, 49949

Offset: 1

Mikk Heidemaa, May 31 2017

For k > 2, numbers such that '37'||...'6'...||'73' ('6' concatenated k-2 times and prefixed by '37', and suffixed by '73') in decimal form is prime.

			13 is in the sequence because (10^13*113 + 19)/3 = 376666666666673 is prime.

Cf. A051919, A101724.

ParallelTable[ If[ PrimeQ[ (10^n*113+19)/3], n, Nothing], {n, 2000}]

isok(n) = isprime((10^n*113 + 19)/3); \\ Michel Marcus, Jul 21 2017

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A051918 Start with n, apply k->2k+1 until reach new record prime; sequence gives number of steps needed.

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A189657 Start with n, apply k->2k+1 until a semiprime is reached; sequence gives the semiprimes.

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A287766 Numbers k such that (10^k*113 + 19)/3 is prime.

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