A239790 The smallest multidigit prime of a sequence of n consecutive primes such that their digit sums are also a sequence of n consecutive primes.

11, 41, 41, 191, 402131, 6340271501

Offset

1,1

Comments

a(7), if it exists, is larger than 2*10^14. - Giovanni Resta, Apr 03 2014

a(7) <= 101100010001001200110001. - Jens Kruse Andersen, Aug 28 2016

Links

Table of n, a(n) for n=1..6.

Números y Algo Más Primos cuya suma digital dan primos

B. Sindelar, Two Sets of Consecutive Primes and their Sum of Digits Connection

Bill Sindelar, Jens Kruse Andersen, Marian Otremba, Two Sets of Consecutive Primes and their Sum of Digits Connection, digest of 12 messages in primenumbers Yahoo group, Aug 26 - Aug 30, 2016.

Example

a(4)=191 because 191, 193, 197, 199 generates 11, 13, 17, 19.
a(5)=402131 because 402131, 402133, 402137, 402139, 402197 generates 11,13,17,19,23.

Prog

(UBASIC)
   10   P=7:KM=0:'puzzle 1290, Meller
   20   P=nxtprm(P):if P>2^32-20 then end
   30   gosub *K:if K<=KM then goto 20
   40   print K, P, Q1:KM=K:goto 20
  100   *K
  110   Z=P:gosub *SODZ
  120   if SODZ<>prmdiv(SODZ) then return
  130   K=1:Q=SODZ:Q1=Q
  140   Z=nxtprm(Z):gosub *SODZ
  150   if SODZ<>nxtprm(Q) then return
  160   K=K+1:Q=nxtprm(Q):goto 140
  200   *SODZ:SODZ=0:L=alen(Z)
  210   for I=1 to L:D=val(mid(str(Z), I+1, 1))
  220   SODZ=SODZ+D:next I
  230   return

Crossrefs

Cf. A007953, A046704, A240598.

Sequence in context: A089348 A088622 A121171 * A065079 A065049 A158201

Adjacent sequences: A239787 A239788 A239789 * A239791 A239792 A239793

Keyword

nonn,base,hard

Author

Carlos Rivera, Mar 26 2014

Extensions

a(6) from Giovanni Resta, Apr 03 2014

Status

approved