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A247896 Primes that produce a different prime when one of its digits is added to it. 1
29, 43, 61, 67, 89, 167, 227, 239, 263, 269, 281, 349, 367, 389, 439, 457, 461, 463, 487, 499, 521, 563, 601, 607, 613, 641, 643, 647, 653, 677, 683, 821, 827, 983, 1063, 1229, 1277, 1283, 1289, 1361, 1367, 1423, 1427, 1429, 1447, 1481, 1483, 1489, 1549, 1601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From an idea of Eric Angelini (see seqfan link).

Digit 0 is not considered because the new primes must be different from the starting numbers. Therefore, 101 is not part of the sequence, because the only prime that results from adding one of its digits is 101 + 0 = 101, which is the same number, while 601 is acceptable because 601 + 6 = 607, a prime.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Eric Angelini, Primes adding one of their digit to themselves (+chains)

EXAMPLE

The number 29 is prime, and 29 + 2 = 31 is also prime.

The same with 487, which produces 487 + 4 = 491, a prime.

MAPLE

P:=proc(q) local a, b, k, n, ok;

for n from 1 to q do a:=ithprime(n); ok:=0;

for k from 1 to ilog10(a)+1 do

b:=trunc((a mod 10^k)/10^(k-1)); if b>0 then

if isprime(a+b) then ok:=1; break; fi; fi; od;

if ok=1 then print(a); fi; od; end: P(10^6);

PROG

(PARI) /* Description: Generates a vector containing this kind of terms between m^u1 and m^u2 for this definition applied by adding base B digits to the original number in decimal. Here (u1, m, B)=(1, 3, 10) by default. */

LstThem(u2, u1=1, m=3, B=10)={

my(L:list=List(), y);

forprime(x=m^u1, m^u2,

y=vecsort(digits(x, B), , 8);

if(sum(j=1, #y, y[j]&&isprime(x+y[j])),

listput(L, x)));

vector(#L, i, L[i])} \\ R. J. Cano, Sep 27 2014

(Haskell)

a247896 n = a247896_list !! (n-1)

a247896_list = filter f a000040_list where

f p = any ((== 1) . a010051') $

map (+ p) $ filter (> 0) $ map (read . return) $ show p

-- Reinhard Zumkeller, Sep 27 2014

CROSSREFS

Cf. A047791, A048519.

Cf. A000040, A010051.

Sequence in context: A341658 A168474 A341666 * A162357 A316741 A173967

Adjacent sequences: A247893 A247894 A247895 * A247897 A247898 A247899

KEYWORD

nonn,easy,base

AUTHOR

Paolo P. Lava, Sep 26 2014

STATUS

approved

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)