A240598 -id:A240598 - cp's OEIS frontend

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

Carlos Rivera, Mar 26 2014

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

			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.

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.

Cf. A007953, A046704, A240598.

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

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

a(6) from Giovanni Resta, Apr 03 2014

A241525 a(n) is the smallest start of a run of exactly n consecutive primes such that the sum of the digits of each prime is composite.

Original entry on oeis.org

19, 17, 13, 521, 509, 503, 499, 491, 14153, 25793, 25771, 37663, 37657, 98729, 98717, 98713, 98711, 98689, 98669, 98663, 98641, 98639, 98627, 98621, 98597, 98573, 69794393, 69794383, 268684679, 268684651, 268684627, 329788829, 545497787, 545497769, 545497759, 545497753, 545497747, 545497741, 545497727, 545497723, 545497691, 545497681, 545497679, 545497637, 545497633, 545497609

Offset: 1

Carlos Rivera, Apr 24 2014

No more terms below 2^32

			a(3)=13 because the run of the 3 consecutive primes {13, 17, 19} is such that the sum of digits for each prime is {4, 8, 10}.

Cf. A240598.

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

cp's OEIS Frontend

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.

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