A181503
Slowest-growing sequence of primes p where 1/(p+1) sums to 1 without actually reaching it.
Original entry on oeis.org
2, 3, 5, 7, 11, 29, 127, 1931, 309121, 47777896349, 76090912606600214447, 120621395443859821620817698234224534627, 63813688766771960235613705494151343867425896610637722399417500492543759703
Offset: 1
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a[n_] := a[n] = Block[{sm = Sum[1/(a[i] + 1), {i, n - 1}]}, NextPrime[ Max[ a[n - 1], 1/(1 - sm)]]]; a[0] = 1; Array[a, 15] (* Robert G. Wilson v, Oct 27 2010 *)
A225669
Slowest-growing sequence of odd primes whose reciprocals sum to 1.
Original entry on oeis.org
3, 5, 7, 11, 13, 17, 19, 23, 967, 101419, 2000490719, 106298338760698351, 586903266015193517540253132922939, 3494365451928289992209032562272585187947069047023572601254975717
Offset: 1
Since 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 < 1, the first eight odd primes are members. The ninth is not, because adding 1/29 pushes the sum over 1.
- Popular Computing (Calabasas, CA), Problem 175: A Sum of a Different Kind, Vol. 5 (No. 50, May 1977), p. PC50-8.
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a[n_] := a[n] = Block[{sm = Sum[1/(a[i]), {i, n - 1}]}, NextPrime[ Max[ a[n - 1], 1/(1 - sm)]]]; a[0] = 2; Array[a, 14]
A225670
Slowest-growing sequence of odd primes p where 1/(p+1) sums to 1 without actually reaching it.
Original entry on oeis.org
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 2539, 936599, 127852322431, 510819260848900502567, 1553192364608434843485965159509450536731, 52119893982548112392303882371161186032080710958633917215400463948724068502699
Offset: 1
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a[n_] := a[n] = Block[ {sm = Sum[ 1/(a[i] + 1), {i, n - 1}]}, NextPrime[ Max[ a[n - 1], 1/(1 - sm)]]]; a[0] = 2; Array[ a, 20]
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