A052028 -id:A052028 - cp's OEIS frontend

A052065 a(n) is the first square root greater than 10^n such that a(n)^2 is a palfree square (palfree = contains no palindromic substring except single digits).

13, 104, 1014, 10123, 101047, 1010456, 10104574, 101045587, 1010455851, 10104558492, 101045584913, 1010455848322, 10104558481373, 101045584813152, 1010455848130452, 10104558481304484

Offset: 1

Patrick De Geest, Jan 15 2000

Probably finite.

Keith Schneider, Table of n, a(n) for n = 1..25
Keith Schneider, Mathematica code for A052025-A052028

Cf. A052066, A052061, A052062.

More terms from Keith Schneider (schneidk(AT)email.unc.edu), May 23 2007

A256351 Composites in base 10 that remain composite in exactly seven bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

8, 9, 15, 16, 21, 22, 25, 28, 34, 75, 87, 91, 93, 94, 106, 111, 123, 141, 143, 145, 147, 155, 172, 201, 205, 214, 217, 237, 255, 298, 304, 305, 363, 371, 376, 377, 385, 388, 395, 403, 411, 423, 428, 442, 458, 466, 471, 473, 483, 495, 501, 505, 507, 531, 533

Offset: 1

Sebastian Petzelberger, Mar 25 2015

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
Carlos Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A052026, A256350 - A256356.
Cf. A038537, A052027, A052028, A052029, A052030, A052031, A052032, A084482.
Cf. A052033, A236356.

f:= proc(b,x) local L,i;
L:= convert(x,base,b);
isprime(add(10^(i-1)*L[i],i=1..nops(L)))
end proc:
select(t -> not isprime(t) and nops(select(f,[$2..9],t))=2, [$1..1000]); # Robert Israel, Mar 26 2015

fQ[n_] := CompositeQ@ n && Count[ CompositeQ[ FromDigits[ IntegerDigits[n, #]] & /@ Range[2, 9]], True] == 6; Select[ Range@ 500, fQ] (* Robert G. Wilson v, Mar 26 2015 *)

A052066 Palfree squares whose root is the smallest possible greater than 10^n (palfree = contains no palindromic substring except single digits).

Original entry on oeis.org

169, 10816, 1028196, 102475129, 10210496209, 1021021327936, 102102415721476, 10210210652174569, 1021021026820134201, 102102102318249314064, 10210210230410293217569

Offset: 1

Patrick De Geest, Jan 15 2000

Probably finite.

Keith Schneider, Table of n, a(n) for n = 1..25
Keith Schneider, Mathematica code for A052025-A052028

Cf. A052065, A052061, A052062.

More terms from Keith Schneider (schneidk(AT)email.unc.edu), May 23 2007

A052067 a(n) is the first cube root greater than 10^n such that a(n)^3 is a palfree cube (palfree = contains no palindromic substring except single digits).

Original entry on oeis.org

12, 102, 1008, 10091, 100698, 1007059, 10069605, 100695969, 1006958659, 10069585741, 100695847434, 1006958474563, 10069584743393, 100695847434688, 1006958474332019, 10069584743315203

Offset: 1

Patrick De Geest, Jan 15 2000

Probably finite.

Keith Schneider, Table of n, a(n) for n = 1..25
Keith Schneider, Mathematica code for A052025-A052028

Cf. A052068, A052063, A052064.

More terms from Keith Schneider (schneidk(AT)email.unc.edu), May 23 2007

A052068 Palfree cubes whose root is the smallest possible greater than 10^n (palfree = contains no palindromic substring except single digits).

Original entry on oeis.org

1728, 1061208, 1024192512, 1027549183571, 1021086501268392, 1021326840189306379, 1021027182906953620125, 1021024718963175618538209, 1021021582763927831895785179

Offset: 1

Patrick De Geest, Jan 15 2000

Probably finite.

Keith Schneider, Table of n, a(n) for n = 1..25
Keith Schneider, Mathematica code for A052025-A052028

Cf. A052067, A052063, A052064.

More terms from Keith Schneider (schneidk(AT)email.unc.edu), May 23 2007

A256355 Composites in base 10 that remain composite in exactly three bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

Original entry on oeis.org

11233, 42241, 98281, 131239, 161953, 315151, 358135, 606553, 692263, 785851, 1114081, 1130419, 1525777, 1906363, 3369313, 3403081, 3880873, 5616721, 6036103, 6947611, 7253191, 7516783, 7886593, 8799127, 8811223, 9108289, 9113203, 9195313, 9450361, 9600769

Offset: 1

Sebastian Petzelberger, Mar 25 2015

			11233 = 324413_5 and 324413_10 is composite; 11233 = 44515_7 and 44515_10 is composite; 11233_10 itself is composite. Interpreted in base 2, 3, 4, 6, 8, and 9 the result is prime. Hence 11233 is in this sequence.

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
Carlos Rivera, PP&P Puzzle 24: Primes in several bases

Cf. A052026, A256350, A256351, A256352, A256353, A256354, A256356, A038537, A052027, A052028, A052029, A052030, A052031, A052032, A052033, A084482, A236356.

is(n)=!isprime(n) && sum(b=2,9,isprime(fromdigits(digits(n,b))))==6 \\ Charles R Greathouse IV, Apr 23 2015

cp's OEIS Frontend

A052065 a(n) is the first square root greater than 10^n such that a(n)^2 is a palfree square (palfree = contains no palindromic substring except single digits).

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A256351 Composites in base 10 that remain composite in exactly seven bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

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Maple

Mathematica

A052066 Palfree squares whose root is the smallest possible greater than 10^n (palfree = contains no palindromic substring except single digits).

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A052067 a(n) is the first cube root greater than 10^n such that a(n)^3 is a palfree cube (palfree = contains no palindromic substring except single digits).

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A052068 Palfree cubes whose root is the smallest possible greater than 10^n (palfree = contains no palindromic substring except single digits).

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Comments

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Crossrefs

Extensions

A256355 Composites in base 10 that remain composite in exactly three bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

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Programs

PARI