A108606 -id:A108606 - cp's OEIS frontend

A108605 Semiprimes with prime sum of factors: twice the lesser of the twin prime pairs.

6, 10, 22, 34, 58, 82, 118, 142, 202, 214, 274, 298, 358, 382, 394, 454, 478, 538, 562, 622, 694, 838, 862, 922, 1042, 1138, 1198, 1234, 1282, 1318, 1618, 1642, 1654, 1714, 1762, 2038, 2062, 2098, 2122, 2182, 2302, 2458, 2554, 2578, 2602, 2638, 2854, 2902

Offset: 1

Zak Seidov, Jun 12 2005

All terms are even. (Cf. formula.)
The definition implies that the sum of factors is the sum over the prime factors with multiplicity, as in A001414. - R. J. Mathar, Nov 28 2008
The sum of factors of a semiprime pq is p+q, which can only be prime if {p, q} = {2, odd prime}. Requiring the sum to be prime then implies that the semiprime is twice the lesser of a twin prime pair. - M. F. Hasler, Apr 07 2015
Subsequence of A288814, each term being of the form A288814(p), where p is the greatest of a pair of twin primes. - David James Sycamore, Aug 29 2017

			58=2*29 and 2+29 is prime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A001358 semiprimes, A001359 lesser of twin primes, A101605 3-almost primes, A108606 semiprimes with prime sum of digits, A108607 intersection of A108605 and A108606.

Select[Range[2, 3000, 2], !IntegerQ[Sqrt[ # ]]&&Plus@@(Transpose[FactorInteger[ # ]])[[2]]==2&&PrimeQ[Plus@@(Transpose[FactorInteger[ # ]])[[1]]]&]
Select[Range[2,3000,2],PrimeOmega[#]==PrimeNu[#]==2&&PrimeQ[Total[ FactorInteger[ #][[;;,1]]]]&] (* Harvey P. Dale, Apr 10 2023 *)

list(lim)=my(v=List(),p=2); forprime(q=3,lim\2+1, if(q-p==2, listput(v,2*p)); p=q); Vec(v) \\ Charles R Greathouse IV, Feb 05 2017

a(n)=2*p, with p and 2+p twin primes: a(n)=2*A001359(n).

Changed division by 2 to multiplication by 2 in formula related to A001359. - R. J. Mathar, Nov 28 2008

A084995 Numbers which can be written as the product of two different primes and the sum of digits is also prime.

Original entry on oeis.org

14, 21, 34, 38, 58, 65, 74, 85, 94, 106, 111, 115, 119, 122, 133, 142, 146, 155, 166, 201, 203, 205, 209, 214, 218, 221, 247, 254, 265, 274, 278, 287, 298, 302, 319, 326, 335, 346, 355, 362, 371, 377, 382, 386, 391, 395, 403, 407, 427, 445, 454, 458, 469, 478, 481, 485

Offset: 1

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 30 2003

			E.g., 14 = 7*2 and 1+4 = 5 is also prime.

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Cf. A006881, A028834, A108606.

Module[{nn=60},Select[Union[Times@@@Subsets[Prime[Range[nn]],{2}]],PrimeQ[ Total[ IntegerDigits[#]]]&&#<=2Prime[nn]&]] (* Harvey P. Dale, Feb 28 2022 *)

is(n)={bigomega(n)==2 && !issquare(n) && isprime(sumdigits(n))}
select(is, [1..500]) \\ Andrew Howroyd, Jan 05 2020

Intersection of A028834 and A006881. - Andrew Howroyd, Jan 05 2020

Terms a(14) and beyond from Andrew Howroyd, Jan 05 2020

A108610 Semiprimes with prime sum of decimal digits and prime sum of prime factors.

Original entry on oeis.org

34, 58, 142, 214, 274, 298, 382, 454, 478, 562, 694, 838, 922, 1042, 1138, 1198, 1282, 1318, 1642, 1714, 2038, 2098, 2122, 2182, 2302, 2458, 2638, 2854, 2902, 2962, 3334, 3394, 3442, 3574, 3754, 3862, 4054, 4162, 4258, 4474, 4618, 4762, 5314, 5374, 5422

Offset: 1

Zak Seidov, Jun 12 2005

Intersection of A108605 and A108606. All terms are even. Cf. A001358 semiprimes, A101605 3-almost primes, A108605 semiprimes with prime sum of factors, A108606 semiprimes with prime sum of digits.

			34=2*17 (semiprime), with 3+4=7 and 2+17=19 both prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001358, A101605, A108605, A108606.

psddQ[n_]:=!IntegerQ[Sqrt[n]]&&PrimeOmega[n]==2&&PrimeQ[Total[ IntegerDigits[n]]] && PrimeQ[Total[Transpose[FactorInteger[n]][[1]]]]; Select[Range[5500],psddQ] (* Harvey P. Dale, Oct 03 2012 *)

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A108605 Semiprimes with prime sum of factors: twice the lesser of the twin prime pairs.

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A084995 Numbers which can be written as the product of two different primes and the sum of digits is also prime.

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A108610 Semiprimes with prime sum of decimal digits and prime sum of prime factors.

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Mathematica