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A345904 Numbers ending in 1, 3, 7 or 9 that yield no primes if their first digit is changed to another nonzero digit. 1
1071, 1149, 1183, 1401, 1509, 1611, 1771, 1773, 1809, 1891, 1921, 2071, 2149, 2183, 2401, 2509, 2611, 2771, 2773, 2809, 2891, 2921, 3071, 3149, 3183, 3401, 3509, 3611, 3771, 3773, 3809, 3891, 3921, 4071, 4149, 4183, 4401, 4509, 4611, 4771, 4773, 4809, 4891, 4921, 5071 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If a number is in this sequence, then all the numbers with the first digit changed to another nonzero digit are also in this sequence.

Numbers ending in 0, 2, 4, 5, 6, and 8 are not included by definition, because they are composite independently of the other digits.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

1071, 2071, 3071, 4071, 5071, 6071, 7071, 8071 and 9071 are all composite numbers. Thus, all of them are in this sequence.

MAPLE

q:= n-> (l-> l[1] in [1, 3, 7, 9] and andmap(not isprime, [seq(parse

   (cat(j, seq(l[-i], i=2..nops(l)))), j=1..9)]))(convert(n, base, 10)):

select(q, [$1..5080])[];  # Alois P. Heinz, Jun 29 2021

MATHEMATICA

Select[Range[1, 6000, 2], Take[IntegerDigits[#], -1] != {5} && CompositeQ[Table[FromDigits[Prepend[Rest[IntegerDigits[#]], n]], {n, 9}]] == {True, True, True, True, True, True, True, True, True} &]

Select[Range[1, 5100, 2], NumberDigit[#, 0]!=5&&NoneTrue[FromDigits/@Table[ PadRight[ {d}, IntegerLength[#], IntegerDigits[#]], {d, 9}], PrimeQ]&] (* Harvey P. Dale, Sep 24 2021 *)

PROG

(Python)

from sympy import isprime

def ok(n):

    if n < 10 or n%10 not in {1, 3, 7, 9}: return False

    s = str(n)[1:]

    return all(not isprime(int(d+s)) for d in "123456789")

print(list(filter(ok, range(1, 6000, 2)))) # Michael S. Branicky, Jun 29 2021

CROSSREFS

Subsequence of A045572.

Sequence in context: A252569 A020386 A236870 * A252256 A345525 A345779

Adjacent sequences:  A345901 A345902 A345903 * A345905 A345906 A345907

KEYWORD

nonn,base

AUTHOR

Tanya Khovanova, Jun 29 2021

STATUS

approved

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Last modified January 27 10:14 EST 2022. Contains 350607 sequences. (Running on oeis4.)