A395346 - OEIS

A395346

Primes that begin a pair of consecutive primes with the same number of digits and a prime-valued digit dot product.

19, 23, 37, 41, 43, 47, 61, 79, 131, 137, 193, 223, 227, 229, 263, 277, 281, 311, 313, 317, 353, 397, 409, 421, 443, 457, 463, 499, 601, 643, 677, 691, 809, 811, 821, 823, 827, 829, 863, 877, 881, 883, 971, 1013, 1031, 1033, 1093, 1103, 1153, 1163, 1171, 1181

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

19 is included because it is followed by the prime 23, both are two-digit numbers, and their digit dot product 1*2 + 9*3 = 29 which is prime.

MAPLE

q:= 2: Lq:= [2]: nq:= 1: count:= 0: R:= NULL:

while count < 100 do

p:= q; Lp:= Lq; np:= nq;

q:= nextprime(p); Lq:= convert(q, base, 10); nq:= nops(Lq);

if np = nq and isprime(add(Lp[i]*Lq[i], i=1..np)) then R:= R, p; count:= count+1 fi

od:

R; # Robert Israel, Apr 20 2026

MATHEMATICA

q[p_] := IntegerLength[p[[1]]] == IntegerLength[p[[2]]] && PrimeQ[IntegerDigits[p[[1]]].IntegerDigits[p[[2]]]]; Select[Partition[Prime[Range[200]], 2, 1], q][[;; , 1]] (* Amiram Eldar, Apr 20 2026 *)

PROG

(PARI) is(p)=my(q=nextprime(p+1), u=digits(p), v=digits(q)); if(#u==#v, my(r=u*v~); return(ispseudoprime(r))); 0

CROSSREFS

Cf. A000040, A033994, A337574.

Sequence in context: A384923 A343741 A060269 * A245382 A075585 A052030

Adjacent sequences: A395343 A395344 A395345 * A395347 A395348 A395349

KEYWORD

nonn,base

AUTHOR

Jean-Marc Rebert, Apr 20 2026

STATUS

approved