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A356273
a(n) is the position of the least prime in the ordered set of numbers obtained by inserting/placing any digit anywhere in the digits of n (except a zero before 1st digit), or 0 if there is no prime in that set.
1
2, 5, 1, 5, 8, 7, 1, 11, 1, 2, 1, 10, 1, 14, 7, 10, 1, 10, 1, 0, 4, 7, 4, 7, 8, 11, 1, 11, 4, 10, 1, 0, 2, 14, 11, 16, 1, 14, 1, 5, 2, 7, 8, 11, 16, 11, 3, 19, 1, 8, 1, 8, 3, 10, 17, 14, 1, 20, 3, 7, 4, 0, 1, 11, 14, 13, 1, 17, 2, 8, 2, 16, 1, 14, 13, 14, 2, 22, 1, 17
OFFSET
1,1
COMMENTS
It appears that a(n) = 0 for n in A124665.
891, a term of A124665 and with a(891) = 9, is the first counterexample. - Michael S. Branicky, Aug 01 2022
LINKS
EXAMPLE
For n=1, the resulting set is (10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91) where the least prime 11 is at position 2, so a(1) = 2.
For n=2, the resulting set is (12, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 42, 52, 62, 72, 82, 92) where the least prime 23 is at position 5, so a(2) = 5.
MATHEMATICA
Table[Function[w, If[IntegerQ[#], #, 0] &@ FirstPosition[Rest@ Union@ Flatten@ Table[FromDigits@ Insert[w, d, k], {k, Length[w] + 1, 1, -1}, {d, 0, 9}], _?PrimeQ][[1]]][IntegerDigits[n]], {n, 80}] (* Michael De Vlieger, Aug 01 2022 *)
PROG
(PARI) get(d, rd, n, k) = {if (n==0, return(fromdigits(concat(d, k)))); if (n==#d, return(fromdigits(concat(k, d)))); my(v = concat(Vec(d, #d-n), k)); v = concat(v, Vecrev(Vec(rd, n))); fromdigits(v); }
a(n) = {my(d=digits(n), rd = Vecrev(d), list = List(), p); for (n=0, #d, my(kstart = if (n==#d, 1, 0)); for (k=kstart, 9, listput(list, get(d, rd, n, k)); ); ); my(svec = Set(Vec(list))); for (k=1, #svec, if (isprime(svec[k]), return(k)); ); }
(Python)
from sympy import isprime
def a(n):
s = str(n)
out = set(s[:i]+c+s[i:] for i in range(len(s)+1) for c in "0123456789")
out = sorted(int(k) for k in out if k[0] != "0")
ptest = (i for i, k in enumerate(sorted(out), 1) if isprime(int(k)))
return next(ptest, 0)
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Aug 01 2022
CROSSREFS
Related to the process in A068166, A068167, A068169, A068170, A068171, A068172, A068173, and A068174.
Cf. A124665.
Sequence in context: A289848 A258020 A021803 * A077382 A046527 A008343
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Aug 01 2022
STATUS
approved