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A250312 Numbers which produce primes if their divisors, one by one, are prepended, inserted or appended. 3
1, 151, 157, 169, 223, 277, 283, 337, 361, 367, 397, 409, 421, 439, 457, 469, 547, 571, 577, 589, 607, 643, 673, 709, 757, 769, 793, 871, 877, 937, 1063, 1093, 1201, 1603, 1609, 1807, 2029, 2053, 2071, 2707, 3019, 3037, 3049, 3073, 3109, 3607, 4039, 4051, 4087 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

EXAMPLE

Divisors of 1 is 1 and concat(1,1) = 11 is prime.

Divisors of 151 are 1, 151. Then concat(151,1) = 1511 is prime, as is concat(1,151) = 1151, and concat(1,151,51) = 115151 is prime.

Divisors of 169 are 1, 13, 169. Then concat(16,1,9) = 1619 is prime, concat(16,13,9) = 16139 is prime, as is concat(1,13,69) = 11369, and concat(1,169,69) = 116969 is prime.

MAPLE

with(numtheory): P:=proc(q) local a, b, c, f, g, h, j, k, n;

for n from 1 by 2 to q do a:=divisors(n); h:=0;

for k from 1 to nops(a) do b:=ilog10(a[k])+1;

for j from 0 to ilog10(n)+1 do f:=(n mod 10^j);

if j=0 then c:=n*10^b+a[k]; else g:=a[k]*10^(ilog10(f)+1)+f;

c:=trunc(n/10^j)*10^(ilog10(g)+1)+g; fi;

if isprime(c) then h:=h+1; break; fi; od;

if h=nops(a) then print(n); fi; od; od; end: P(10^6);

CROSSREFS

CF. A250311.

Sequence in context: A115483 A182875 A336777 * A180554 A243531 A139505

Adjacent sequences:  A250309 A250310 A250311 * A250313 A250314 A250315

KEYWORD

nonn,base,easy

AUTHOR

Paolo P. Lava, Nov 18 2014

EXTENSIONS

Inserted a(3), a(16) and a(26) by Paolo P. Lava, Nov 21 2014

STATUS

approved

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Last modified September 25 05:14 EDT 2021. Contains 347652 sequences. (Running on oeis4.)