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User: Ali Adams

Ali Adams has authored 2 sequences.

A329522 Composite numbers whose sum of digits is not composite.

10, 12, 14, 16, 20, 21, 25, 30, 32, 34, 38, 49, 50, 52, 56, 58, 65, 70, 74, 76, 85, 92, 94, 98, 100, 102, 104, 106, 110, 111, 115, 119, 120, 122, 124, 128, 133, 140, 142, 146, 148, 155, 160, 164, 166, 175, 182, 184, 188, 200, 201, 203, 205, 209, 210, 212, 214, 218, 221, 230

Offset: 1

Ali Adams, Nov 15 2019

Cf. A046704, A104213, A141642, A228019.

[k:k in [2..230]| not IsPrime(k) and (IsPrime(&+Intseq(k)) or &+Intseq(k) eq 1) ]; // Marius A. Burtea, Feb 05 2020

Select[Rest@ Complement[#, Prime@ Range@ PrimePi@ Max@ #] &@ Range@ 230, ! CompositeQ@ Total@ IntegerDigits@ # &] (* Michael De Vlieger, Nov 15 2019 *)
Select[Range[250],CompositeQ[#]&&!CompositeQ[Total[IntegerDigits[#]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 19 2021 *)

lista(nn) = forcomposite(c=1, nn, my(s=sumdigits(c)); if ((s==1) || isprime(s), print1(c, ", "))); \\ Michel Marcus, Nov 15 2019

A260981 Primes p that are equal to the sum of the first k primes where p=prime(prime(k)).

Original entry on oeis.org

5, 17, 41

Offset: 1

Waleed Mohammed, Ali Adams, Aug 06 2015

Terms listed are the only three primes p found to satisfy the condition that p = prime(m) = Sum_{i=1..k} prime(i) where m=prime(k).
From Jon E. Schoenfield, Aug 19 2015: (Start)
Let S(k) be the sum of the first k primes, and let PP(k) = prime(prime(k)); then the terms of the sequence are the values of prime(prime(k)) at those values of k at which S(k) = PP(k). (This occurs at k = 2, 4 and 6.)
Given the behavior of the ratio S(k)/PP(k) over the range of values of k shown in the table below, it seems very unlikely that this ratio will return to 1 for any k beyond the values that have been tested, and thus very likely that a(3) = 41 = PP(6) is the final term in the sequence:
     k        S(k)         PP(k)     S(k)/PP(k)
  ======  ===========    ========  ==============
       1            2           3     0.666666...
       2            5  =        5     1
       3           10          11     0.909090...
       4           17  =       17     1
       5           28          31     0.903225...
       6           41  =       41     1
       7           58          59     0.983050...
       8           77          67     1.149253...
       9          100          83     1.204819...
      10          129         109     1.183486...
     ...
     100        24133        3911     6.170544...
    1000      3682913       80917    45.514700...
   10000    496165411     1366661   363.049367...
  100000  62260698721    20491057  3038.432752... (End)

			k=3: prime(3) = 5 = 2+3 = prime(1) + prime(2).
k=7: prime(7) = 17 = 2+3+5+7 = prime(1) + prime(2) + prime(3) + prime(4).
k=13: prime(13) = 41 = 2+3+5+7+11+13 = prime(1) + prime(2) + prime(3) + prime(4) + prime(5) + prime(6).

Cf. A006450, A007504, A013918.

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User: Ali Adams

A329522 Composite numbers whose sum of digits is not composite.

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A260981 Primes p that are equal to the sum of the first k primes where p=prime(prime(k)).

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