A240598 The smallest first term of a sequence of exactly n consecutive prime numbers each of which has the property that its digit sum is prime.

11, 7, 5, 3, 2, 2063, 3253, 3251, 14293, 2442191, 2442179, 2442173, 2442151, 2442133, 2442113, 466343539, 793234063, 10158613657, 5200298339, 281201652541, 3140590111859, 1523243332991, 1631014452929, 1008266115029

Offset

1,1

Comments

There is no requirement on the order of primes that arise as the digit sums.

a(25) > 2*10^13. - Giovanni Resta, Apr 09 2014

Links

Table of n, a(n) for n=1..24.

Example

a(15) = 2442113 because each of the following fifteen consecutive primes {2442113, 24422133, 2442151, 2442173, 2442179, 2442191, 2442197, 2442199, 2442227, 2442263, 2442287, 2442289, 2442311, 2442353, 2442359} has a sum of digits producing another prime number and the smallest is 2442113.
a(17) = 793234063  because each of the following seventeen consecutive primes {793234063 793234067 793234111 793234139 793234153 793234171 793234177 793234193 793234207 793234243 793234261 793234289 793234333 793234357 793234391 793234427 793234441} has a sum of digits producing another prime number and the smallest is 793234063.

Prog

(UBASIC)
   10   P=1:KM=0:K=0:'puzzle 1290, Meller
   20   P=nxtprm(P):if P>2^32-20 then end
   30   gosub *SODP:if S=prmdiv(S) then K=K+1:Q=P:goto 20
   40   if K>KM then print K, Q:KM=K
   50   K=0:goto 20
  200   *SODP:S=0:L=alen(P)
  210   for I=1 to L:D=val(mid(str(P), I+1, 1))
  220   S=S+D:next I
  230   return

Crossrefs

Cf. A239790.

Sequence in context: A236546 A155914 A087896 * A144262 A110093 A282345

Adjacent sequences: A240595 A240596 A240597 * A240599 A240600 A240601

Keyword

nonn,more,base

Author

Carlos Rivera, Apr 08 2014

Extensions

a(18)-a(24) from Giovanni Resta, Apr 09 2014

Status

approved