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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.)