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
a(7) <= 1212030150560200001. - Oscar Volpatti, Aug 25 2025
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.
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
(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
CROSSREFS
KEYWORD
nonn,base,hard,more
AUTHOR
Carlos Rivera, Mar 26 2014
EXTENSIONS
a(6) from Giovanni Resta, Apr 03 2014
STATUS
approved