proposed

approved

editing

proposed

Primes of the form resulting from (sum of digits of n k) + (sum of digits of prime(nk)) as k runs through the positive integers.

If n=1 and prime=2, then 1+2=3(prime)=a(1). If n=2 and prime=3, then 2+3=5(prime)=a(2). If n=3 and prime=5, then 3+5=8=composite. If n=4 and prime=7, then 4+7=11(prime)=a(3). If n=5 and prime=11, then 5+1+1=7(prime)=a(4), etc.

k=1 yields a term: prime(1) = 2 and 1 + 2 = 3 is prime, so a(1)=3;

k=2 yields a term: prime(2) = 3 and 2 + 3 = 5 is prime, so a(2)=5;

k=3 does not yield a term: prime(3) = 5 and 3 + 5 = 8 is composite;

k=4 yields a term: prime(4) = 7 and 4 + 7 = 11 is prime, so a(3)=11;

k=5 yields a term: prime(5) = 11 and 5 + 1 + 1 = 7 is prime, so a(4)=7.

Contribution from R. J. Mathar, May 05 2010: (Start)

for n from 1 to 300 do a := A007953(n) +A007953(ithprime(n)) ; if isprime(a) then printf("%d, ", a ) ; end if; end do: (End)# _R. J. Mathar_, May 05 2010

Name corrected and Example section edited by Jon E. Schoenfield, Feb 11 2019

approved

editing

editing

approved

sod[n_]:=Total[IntegerDigits[n]]; Select[Table[sod[n]+sod[Prime[n]], {n, 300}], PrimeQ] (* Harvey P. Dale, Dec 11 2012 *)

approved

editing

_Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), _, Jan 12 2009

Contribution from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, May 05 2010: (Start)

Corrected from a(35) onwards by _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, May 05 2010

3, 5, 11, 7, 13, 17, 23, 13, 23, 23, 13, 17, 23, 29, 19, 17, 29, 23, 17, 19, 23, 29, 23, 19, 31, 23, 17, 19, 29, 31, 31, 23, 11, 19, 19, 17, 19, 23, 17, 17, 17, 23, 29, 31, 23, 29, 23, 13, 19, 19, 31, 31, 23, 23, 17, 11, 31, 29, 23, 13, 23, 29, 23, 29, 29, 19, 23, 31, 37, 23, 29, 37, 17

Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 05 2010: (Start)

A007953 := proc(n) add(d, d=convert(n, base, 10)) ; end proc:

for n from 1 to 300 do a := A007953(n) +A007953(ithprime(n)) ; if isprime(a) then printf("%d, ", a ) ; end if; end do: (End)

Corrected from a(35) onwards by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 05 2010

Primes of the form sum of digits of n + sum of digits of prime(n).

3, 5, 11, 7, 13, 17, 23, 13, 23, 23, 13, 17, 23, 29, 19, 17, 29, 23, 17, 19, 23, 29, 19, 31, 23, 17, 19, 29, 31, 31, 23, 11, 19, 19, 17, 19, 23, 17, 17, 17, 23, 29, 31, 23, 29, 23, 13, 19, 19, 31, 31, 31, 29, 23, 13, 23, 29, 23, 29, 29, 19, 23, 31, 37, 23, 29, 37

1,1

If n=1 and prime=2, then 1+2=3(prime)=a(1). If n=2 and prime=3, then 2+3=5(prime)=a(2). If n=3 and prime=5, then 3+5=8=composite. If n=4 and prime=7, then 4+7=11(prime)=a(3). If n=5 and prime=11, then 5+1+1=7(prime)=a(4), etc.

Cf. A000040.

nonn,base

Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jan 12 2009

approved