A052025 -id:A052025 - 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

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

A258032 Primes p such that p^3 with the rightmost digit removed is also prime.

Original entry on oeis.org

3, 17, 53, 113, 157, 233, 257, 277, 353, 359, 379, 397, 677, 877, 997, 1039, 1217, 1439, 1613, 1697, 1879, 1973, 1997, 2273, 2417, 2459, 2777, 3257, 3413, 3499, 3517, 3697, 3779, 4073, 4157, 4177, 4339, 4973, 4999, 5077, 5197, 5279, 5639, 5813, 5897, 6277, 6379

Offset: 1

K. D. Bajpai, May 16 2015

			a(2) = 17 is prime: 17^3 = 4913. Removing rightmost digit gives 491 which is prime.
a(3) = 53 is prime: 53^3 = 148877. Removing rightmost digit gives 14887 which is prime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000040, A024770, A052025, A137812, A227916, A227919.

Cf. A010051.

a258032 n = a258032_list !! (n-1)
a258032_list = filter ((== 1) . a010051' . flip div 10. (^ 3)) a000040_list
-- Reinhard Zumkeller, May 18 2015

[p: p in PrimesUpTo(6500) |IsPrime(Floor(p^3/10))]; // Vincenzo Librandi, May 17 2015

Select[Prime[Range[1000]], PrimeQ[Floor[(#^3)/10]] &]

forprime(p=1,10000, if(isprime(floor((p^3)/10)), print1(p,", ")))

A173057 Partial sums of A024770.

Original entry on oeis.org

2, 5, 10, 17, 40, 69, 100, 137, 190, 249, 320, 393, 472, 705, 944, 1237, 1548, 1861, 2178, 2551, 2930, 3523, 4122, 4841, 5574, 6313, 7110, 9443, 11782, 14175, 16574, 19513, 22632, 25769, 29502, 33241, 37034, 40831, 46770, 53963, 61294, 68627

Offset: 1

Jonathan Vos Post, Feb 08 2010

Partial sums of right-truncatable primes, primes whose every prefix is prime (in decimal representation). The sequence has 83 terms. The subsequence of prime partial sums of right-truncatable primes begins: 2, 5, 17, 137, 1237, 1861, 2551, 199483. What is the largest value in the subsubsequence of right-truncatable prime partial sums of right-truncatable primes?

			a(50) = 2 + 3 + 5 + 7 + 23 + 29 + 31 + 37 + 53 + 59 + 71 + 73 + 79 + 233 + 239 + 293 + 311 + 313 + 317 + 373 + 379 + 593 + 599 + 719 + 733 + 739 + 797 + 2333 + 2339 + 2393 + 2399 + 2939 + 3119 + 3137 + 3733 + 3739 + 3793 + 3797 + 5939 + 7193 + 7331 + 7333 + 7393 + 23333 + 23339 + 23399 + 23993 + 29399 + 31193 + 31379.

Cf. A000040, A024770, A033664, A024785 (left-truncatable primes), A032437, A020994, A052023, A052024, A052025, A050986, A050987, A069866.

A060825 Smallest n-digit left truncatable prime of Henry VIII type.

Original entry on oeis.org

773, 3373, 15647, 121997, 1237547, 12184967, 126934673, 1231633967, 12181833347, 124627266947, 1213536676883, 13264242313613, 129456645661613, 1399335756373613, 12429121339693967, 198615345451813613, 1276812967623946997, 36484957213536676883, 315396334245663786197, 9918918997653319693967, 95918918997653319693967, 357686312646216567629137

Offset: 3

Lekraj Beedassy, Apr 30 2001

			The 11-digit prime a(11) = 12181833347 is the smallest of its kind such that successive deleting of the leftmost digits produces the primes 2181833347, 181833347, 81833347, 1833347, 833347, 33347, 3347, 347, 47, 7.

S. Kahan and S. Weintraub, Left truncatable primes. Journal of Recreational Mathematics, vol. 29, no. 4 (1998), pp. 255-261.

I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
C. K. Caldwell, Left truncatable primes
P. De Geest, The 4260 left-truncatable primes
Index entries for sequences related to truncatable primes

Cf. A024785, A052023, A052025, A055521.

a(2) removed, offset changed to 3 and a(19)-a(24) added using A055521 by Jinyuan Wang, Aug 07 2020

A173060 Partial sums of A024785.

Original entry on oeis.org

2, 5, 10, 17, 30, 47, 70, 107, 150, 197, 250, 317, 390, 473, 570, 683, 820, 987, 1160, 1357, 1580, 1863, 2176, 2493, 2830, 3177, 3530, 3897, 4270, 4653, 5050, 5493, 5960, 6483, 7030, 7643, 8260, 8903, 9550, 10203, 10876, 11559, 12302, 13075, 13872

Offset: 1

Jonathan Vos Post, Feb 08 2010

Partial sums of left-truncatable primes. This sequence has 4260 terms. The subsequence of prime partial sums of left-truncatable primes begins 2, 5, 17, 47, 107, 197, 317, 683, 7643. The subsubsequence of left-truncatable prime partial sums of left-truncatable primes begins 2, 5, 197, 317.

			a(57) = 2 + 3 + 5 + 7 + 13 + 17 + 23 + 37 + 43 + 47 + 53 + 67 + 73 + 83 + 97 + 113 + 137 + 167 + 173 + 197 + 223 + 283 + 313 + 317 + 337 + 347 + 353 + 367 + 373 + 383 + 397 + 443 + 467 + 523 + 547 + 613 + 617 + 643 + 647 + 653 + 673 + 683 + 743 + 773 + 797 + 823 + 853 + 883 + 937 + 947 + 953 + 967 + 983 + 997 + 1223 + 1283 + 1367.

Cf. A000040, A024770 (right-truncatable primes), A024785, A033664, A032437, A020994, A052023, A052024, A052025, A050986, A050987, A173057.

a(n) = SUM[i=1..n] A024785(i) = SUM[i=1..n] {p prime, and every suffix of p in decimal expansion is prime, and no digits are zero}.

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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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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A258032 Primes p such that p^3 with the rightmost digit removed is also prime.

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A173057 Partial sums of A024770.

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A060825 Smallest n-digit left truncatable prime of Henry VIII type.

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A173060 Partial sums of A024785.

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