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

Author

Carlos Rivera, Mar 26 2014

Keywords

• nonn
• base
• hard
• more
• changed

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

a(7) <= 1212030150560200001. - Oscar Volpatti, Aug 25 2025

Examples

			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.
		

Links

• Números y Algo Más, Primos cuya suma digital dan primos
• Carlos Rivera, Puzzle 1229. Set of consecutive primes such that..., The Prime Puzzles & Problems Connection.
• B. Sindelar, Two Sets of Consecutive Primes and their Sum of Digits Connection [Broken link]
• 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.

Crossrefs

Cf. A007953, A046704, A240598.

Programs

PARI

isok(p, n) = if ((p > 10) && isprime(p), my(v=vector(n)); v[1] = p; for (i=2, n, v[i] = nextprime(v[i-1]+1);); my(vs=vector(n, i, sumdigits(v[i]))); if (!isprime(vs[1]), return(0)); for (i=2, n, if (vs[i] != nextprime(vs[i-1]+1), return(0));); return(1););
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Aug 28 2025

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

Extensions

a(6) from Giovanni Resta, Apr 03 2014